{"id":5662,"date":"2022-04-20T14:03:59","date_gmt":"2022-04-20T21:03:59","guid":{"rendered":"https:\/\/studysoup.com\/blog\/?p=5662"},"modified":"2022-04-20T14:03:59","modified_gmt":"2022-04-20T21:03:59","slug":"applications-integrals-mathematics","status":"publish","type":"post","link":"https:\/\/newblog.studysoup.com\/?p=5662","title":{"rendered":"Applications of Integrals in Mathematics"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/PqR8Eke3Ag3_2QBLiVeUYTEAeJqoM7Y2py2uA_ENUSvwmMCqsyRTOvNd7LAS8SozrMNjJNX4MClT-ninKxDHWYIYYBSdgYoNYe4Qhph97aJ4Xju7O5TRR6NONOFBN2YKaZ-hxMnH\" alt=\"applications of integrals\"\/><\/figure>\n\n\n\n<p>Applications of integrals can be tricky- it can be applied to math, science, and engineering, economics etc. If you don\u2019t have the right teacher or <a href=\"https:\/\/studysoup.com\/tsg\/index?utm_source=applicationsofintegralspost&amp;utm_medium=blog&amp;utm_campaign=applicationsofintegralspost\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"textbook survival guide (opens in a new tab)\">textbook survival guide<\/a>, getting lost before exam can be easy.<br><\/p>\n\n\n\n<p>In this guide you\u2019re going to learn how integration is applied in various scenarios, the different types of integrals, and some examples.&nbsp;<br><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Applications of Integrals: What does it mean?<\/strong><\/h2>\n\n\n\n<p>Integrals can be applied in many different areas like math, science, and engineering, statistics,and economics.<\/p>\n\n\n\n<p>&nbsp;In math, we use it to find:<br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><a href=\"https:\/\/studysoup.com\/tsg\/index?utm_source=bannercta&amp;utm_medium=blog&amp;utm_campaign=blogposts\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/studysoup.com\/blog\/wp-content\/uploads\/2022\/04\/StudySoup-Textbook-Survival-Guides.png\" alt=\"textbooksurvivalguides\" class=\"wp-image-5657\" width=\"744\" height=\"248\"\/><\/a><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>The center of mass (Centroid) of an area with curved sides<\/li><li>The area between two curves<\/li><li>The area under a curve<\/li><li>The average value of a curve<\/li><li>Integral transforms like Laplace and Fourier transforms.&nbsp;<\/li><\/ul>\n\n\n\n<p>When speaking about integrals, there are two different types: definite integrals (also called Riemann Integral) and indefinite integrals.<br><\/p>\n\n\n\n<p>In simple terms, a definite integral has definite limits ( defined upper and lower limits\/bounds) which can be represented by:<br><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/cDLHtdT6T68ONZXIfNIlCpsfpoVcDSpDnQb2qKqBToEfUaV-t-KohZM3VdKusmXmerbDwzy4BhBO19cwWTnL2n-5rNT6itj4JkYcu86AhEbYdO0g7nMBKCyymkkKZjHyVZGjpsCz\" alt=\"definite integral\" width=\"164\" height=\"92\"\/><\/figure>\n\n\n\n<p>In contrast to definite integrals, an indefinite integral is an integral which has no limits. This can be represented by:<br><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/vRGhlkxIEzanJqIre3IyVHcqo1I54a-70SM49VFlB3r5HmLOI62yz_icTmzJhkC1srS8PdeZ9n1-ooU6OzAp6EiHMFC_6cjpFKVfFHfDBruX66wkMj567SBsn6TxruwBFxlwyHg5\" alt=\"indefinite integral\" width=\"353\" height=\"83\"\/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=%5Cint%20f(x)dx%3DF(x)%2BC#0\"><\/a>(C is the constant of integration)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solved: Example Problem of Applications of Integrals<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Given a Derivative Function, Integrate to Find the Original Function\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/y5EpNHRtYkw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/studysoup.com\/blog\/wp-content\/uploads\/2022\/04\/Screen-Shot-2022-04-20-at-8.48.10-AM-1.png\" alt=\"applications of integrals problem\" class=\"wp-image-5679\"\/><\/figure>\n\n\n\n<p>The given function is a type of parabola, the graph is as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/awVakBrMQLx7DveTDYjv5F9xjNXJVtkYWxZ7YYKD3qqrFLd5FWz_tU-x7Lf3zyIA43kdSSwiV0_40Gpf6sBMyGhqig5NES0ykTItdccg8H5hOOUYYoZ0vNnSBGBp9AMD7sQa62c2\" alt=\"applications of integrals graph\"\/><\/figure>\n\n\n\n<p>First, take a look at our notes below:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/t2oErc_DfnNALRFT5X4kd-7TW_90RS1-y93IHz8CjQYrGb3bGYi7tAd79iCmi8cwksJ99EpLUv6Isdqcj7N9X2XO84U7JRj-zXVkMlNon3M6NDPWB6tsVBps7OXx4iJ6i8ca7iZL\" alt=\"definite integrals formula\" width=\"353\" height=\"83\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/cjXpPLoDkeTc-hDf6qjkY9FHcfL4lOebyOPMPcrsntA-f4PtQcdvclMSQYYNzHQGVHlE0Jd2u1L2YpZEqjqB7A43SI1mzTOixb2t-eW3lapvP5VzUDP5LNOTCrFmjQ1nbMnt3xaw\" alt=\"applications of integrals problem\" width=\"137\" height=\"38\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/vHW5BdsVJuc1325F3WzY40PuqVHejtnas04TMjku0YDabxjmwsKabt2cuo2tlWQfTfaKuvcD6f_aLch4i0JkMfd8zXjK4nR7ALuhDe0zx6PfqwFp0aQVY9LSzIXANURrcttEvM5o\" alt=\"applications of integrals problem\" width=\"141\" height=\"38\"\/><\/figure>\n\n\n\n<p>We will integrate the given function to get <a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=F(x)%2Bc#0\"><\/a>. We know that <a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=F(1)%3D7#0\"><\/a> using which we will compute the value of the constant of integration. Once we know the value of constant of integration, the next step is to find f(4).<br><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/AwaMVuZVXrMS3ec_tnGiAZASvqjl58i0nYext9yFwE1hGhG6b7xkce9z3oGPW-IK8sm0Zhbg6WmYNNnpgesa8NeKf2puo3uPRWHkORzERnh3pH2NcycjfFf6co_31vKS4wHGXeg-\" alt=\"applications of integrals problem\" width=\"178\" height=\"42\"\/><\/figure>\n\n\n\n<p>1) Knowing all that, let\u2019s integrate <a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=(9x%5E2%2B10x)#0\"><\/a>.To do that, we need to apply the power rule of integration which would be:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/6fN1o_LiSL-4B7LcoCmhDSL3nYEQKvppbTKe5_WbAkEKzlVGzmmFszQS6A0y9Z-Mb44V9-1-a8hT06nbZZ2VeMkAbZ9QEDLQW-xPlZx4aL8BXYlA1knbUBiaYT5ZfgY96s1gZNFY\" alt=\"power rule of integration\" width=\"174\" height=\"47\"\/><\/figure>\n\n\n\n<p>2)&nbsp; Using the power rule,&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/Fj9F2RmYZ5L32PFsw9hDjmjJyiU3YTshdZR9DA3MVPhklTTTmsEhgtBLv7gg8jEm5x9JRAU79qpLCHd-PhWeYdqpBdcy7Q_9Mx1qBljp3ruP39tUni-k08kWWKLrHb_fO38Crzbo\" alt=\"applications of integrals problem\" width=\"441\" height=\"58\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/CvNdtgOnTXOQaA8d83TD9t0Sm89367SJOZkfX8sIbdN8TxvOOkPXiRokopFrLOjJt_uxOT5IJWzNVEALvgP2ak2_qt-6aHUvwUIVyocq3cw0cAoO-AniLq1wFMUiPDhrF2W2JfCb\" alt=\"applications of integrals problem\" width=\"305\" height=\"82\"\/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=%5Crightarrow%20%5Cfrac%7B9x%5E3%7D%7B3%7D%2B%5Cfrac%7B10x%5E2%7D%7B2%7D%2BC#0\"><\/a>&#8230;&#8230;&#8230;&#8230;&#8230;(1)<\/p>\n\n\n\n<p>Thus we got the result of integration.<br><\/p>\n\n\n\n<p>3) Now we will find the value of the constant of integration,&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/plN1c6fmArzIaSjQO4udtBRCDz-rwXiIJGys6Wco-_VIrUcP6Dy07UGyMRQdgcom8aDyLdtl0HbcaLgnSvVfK4Px__IgIKhNfCCE5hvVbDdjGTa4spkMgX0SL73bzic6N52dOfl-\" alt=\"applications of integrals problem\" width=\"141\" height=\"38\"\/><\/figure>\n\n\n\n<p>We know that <a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=F(1)%3D7#0\"><\/a>, hence applying this value to equation(1) we get<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/T0t_guvxcZhwjSJp7rI8u0Q1yS3gc5YN5FqIf7qA8E_1UEKCLNgWCahn_JsV-z6OT6Kq5tpXHL0VgkztW8XW72aUNp2o_wDETKD2AmYm1YrbMC6CfYl4l3L1-Jg6uUhuIL5qU1Tm\" alt=\"applications of integrals problem\" width=\"400\" height=\"65\"\/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=F(1)%3D%5Cfrac%7B9(1)%5E3%7D%7B3%7D%2B%5Cfrac%7B10(1%5E2)%7D%7B2%7D%2BC%3D7#0\"><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/HlThdlnhvUvL444FlPRq2WUVEH3xZdtFPaxILRJsvZf6lE9D7ENADD0RspCj87DqYPxTPt9GTUYe-9jA8lNEUDBBRjzSUVZxbELyCgXnF9qw5Xpec8YsKSL-C-Rs2-umh8pFlHLh\" alt=\"applications of integrals problem\" width=\"302\" height=\"76\"\/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=%5Crightarrow%20%5Cfrac%7B9%7D%7B3%7D%2B%5Cfrac%7B10%7D%7B2%7D%2BC%3D7#0\"><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/MN8pVw7Bml-iiQAFgCvws6mWaJzdPBsGbJizC1osM-I8CF01lyTx2ZoxG5wagxG4NwrvjIkhAdvZjtGRbvGHjZrTkJ3MP4UC5k23wIOeJVT9UN4a58Kriez-w4IV6CjJSvb79w0y\" alt=\"applications of integrals problem\" width=\"268\" height=\"29\"\/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=%5Crightarrow%203%2B5%2BC%3D7#0\"><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/dwCXqcZ4DIu6BDowMm4mnBJBxnjkldIVo5sH7Brd187TyeQrBU-vlnGbz3gKQ4ZundoOQ8_o_GPS65gwm1KWLWPrcv83N2DeRghjYJQh7lqKBuN8UQMTbZ7Heaypot_2aRCCgWOO\" alt=\"applications of integrals problem\" width=\"205\" height=\"27\"\/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=%5Crightarrow%20C%3D7-8#0\"><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/PuYYhZTIYNkfz7NYg-yRxbfJnzVGiIx5_DN1ifK01ZgNlJgDXcdDu7_iUIosMSFb1xH-hx4IEEr-l1i08DYFHOwqYRecOCeJ9_7iBlEfvg_3GNEQdhkloITxVfdW5espHvCVCIhH\" alt=\"applications of integrals problem\" width=\"121\" height=\"27\"\/><\/figure>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=C%3D-1#0\"><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/3VxAZYtp0IuCPM_YjhucggXMSez3QeBf5rcg9f18xyI6z4ynY_qzDF6qn3kC-iS9HhMOFHIt7dFGzgu3mZhATfQAIxXD-zNB9JeyWnGGjRmfM8jGO-jjWx-2uT61Y3mFXIyZ1GMI\" alt=\"applications of integrals problem\" width=\"147\" height=\"50\"\/><\/figure>\n\n\n\n<p>Therefore we found the value of the constant of integration which is <a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=%5Cboxed%7BC%3D-1%7D#0\"><\/a><br><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/VQCiEj3ikmuR-itpz4DojlVC_54m6LivX23hCN-kgUJ3vL4_JBqvMIoucHo4t4lz7PtKBIHlhbu1f1eNahKB1Y71fwrZU4VnvB7fMbk-fRFZL5u3WD5VBtozoX6I6_fCBJAxxM04\" alt=\"constant of integration\" width=\"71\" height=\"38\"\/><\/figure>\n\n\n\n<p>(4) Now we will apply this value of integration constant to <a href=\"https:\/\/www.codecogs.com\/eqnedit.php?latex=F(4)#0\"><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/3Ji8Kv-S9GFDMi7_Kj80juve9wOGIfgZU9fbYElqwotZerHKs2sJe-byO8IFztvNwAvY7k5JzQvJXZc5f7MFaEO49lj7JpKGa4KyzJ_seChQRrjpKDAmUpTngNpABAt8LWK-fAZZ\" alt=\"applications of integrals problem\" width=\"400\" height=\"78\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/cGhave9CxtBeAv8Zgr-2svXrnfQ6n_4gRBytneCdtObhnnegHyO3lPTe-UvxW4VrwaMZB8V_xdlBvy1pz_g-C5X0JFmgJW7wxjAkmdG1yqF444Kwiml3jJRN6UIK41nY5Bws-Du0\" alt=\"applications of integrals problem\" width=\"400\" height=\"35\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Conclusion<\/strong><\/h2>\n\n\n\n<p>This is just one example of many different scenarios. We have to remember in math alone there are numerous applications and in physics even more! Applications of integrals is a topic that takes practice with the <a href=\"https:\/\/studysoup.com\/tsg\/index?utm_source=applicationsofintegralspost&amp;utm_medium=blog&amp;utm_campaign=applicationsofintegralspost\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"right survival guides and experts to help you with solutions (opens in a new tab)\">right survival guides and experts to help you with solutions<\/a>&#8211; you\u2019ll be on the right track.<br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Applications of integrals can be tricky- it can be applied to math, science, and engineering, economics etc. If you don\u2019t have the right teacher or textbook survival guide, getting lost before exam can be easy. In this guide you\u2019re going to learn how integration is applied in various scenarios, the different types of integrals, and [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":5684,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[13,14,15,10,16],"class_list":["post-5662","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math","tag-applications-of-integrals","tag-calculus","tag-integrals","tag-math","tag-pre-calculus"],"_links":{"self":[{"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/posts\/5662","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5662"}],"version-history":[{"count":0,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/posts\/5662\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/"}],"wp:attachment":[{"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5662"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5662"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5662"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}