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MAC 2311C Lecture 7: 8.2 Area of a sad face of Revolution

United States

Calculus with Analytic Geometry I

Mathematics Calculus/Precalc

Davidson Pierre

University of Central Florida

Solid Mechanics

Engineering Analysis-Statics

Structure and Properties of Materials

Principles of Electrical Engineering

Calculus with Analytic Geometry III

Ordinary Differential Equations I

Probability and Statistics for Engineers

Finding the Area of a Surface of Revolution Using Technology
In Exercises 49 and 50, use the integration capabilities of a graphing utility to approximate the area of the surface of revolution.
Function <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/128047986271700/question/0.webp?img=107fa9dd5b4b1bc4add84b825cf7caf4" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/128047986271700/question/0.png?img=1d824e210062126548349c29c8a7fecb" data-mlang="latex" data-equation="y%3Dsinx"></picture>
Interval <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/128047986271700/question/1.webp?img=b21da8fd37ece72591d83e5485ff946b" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/128047986271700/question/1.png?img=f8d049a6ca01ad6c78009584fbde754f" data-mlang="latex" data-equation="lfloor%7B0%2Cpi%7Drfloor"></picture>
Axis of Revolution <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/128047986271700/question/2.webp?img=848301a44c0220bf802324a691657d4d" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/128047986271700/question/2.png?img=32fbf5e18b2acfd2818d8877cbdb2fe5" data-mlang="latex" data-equation="x%5Ctext%7B-axis%7D"></picture>

Finding the Area of a Surface of Revolution Using Technology
In Exercises 49 and 50, use the integration capabilities of a graphing utility to approximate the area of the surface of revolution.
<ul>
<li>Function <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/052336640659051/question/0.webp?img=a8b0c4f2e6cf806d28c50f8bbdc3898a" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/052336640659051/question/0.png?img=f34d8b6fbcd2bf00676fa9463447d4d8" data-mlang="latex" data-equation="y%3Dlnx"></picture>
</li>
<li>Interval <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/052336640659051/question/1.webp?img=7b2436d839917fb10cd210fc24a4b3b3" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/052336640659051/question/1.png?img=269730c643429b77229c3d3b3dd9fb47" data-mlang="latex" data-equation="lbrack1%2Cerbrack"></picture>
</li>
<li>Axis of Revolution  <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/052336640659051/question/2.webp?img=256a0caf423a56ffb79108d292acf570" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/052336640659051/question/2.png?img=09dd9c02ba030f4bfb5965973255fb09" data-mlang="latex" data-equation="y%5Ctext%7B-axis%7D"></picture>
</li>
</ul>

Finding the Area of a Surface of Revolution In Exercises 65-68, find the area of the surface formed by revolving the polar equation over the given interval about the given line.
Polar Equation Interval Axis of Revolution
<picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/022665141031255/question/0.webp?img=f6a4bc2c4dada66d1f7ac28d07b58606" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/022665141031255/question/0.png?img=1b828e80ea77a7ddd653bfcc11a52b8c" data-mlang="latex" data-equation="r%3Dacostheta"></picture> <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/022665141031255/question/1.webp?img=d87bf24f514987b9a7fab988d53a8a3d" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/022665141031255/question/1.png?img=00c29bbf23e107404a43d280e905ff0f" data-mlang="latex" data-equation="0leqthetaleq%5Cfrac%7Bpi%7D%7B2%7D"></picture> <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/022665141031255/question/2.webp?img=67c9f8ccfa02cf8daffb46f5629f821b" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/022665141031255/question/2.png?img=a75936008f917ba87a230dd09d70556a" data-mlang="latex" data-equation="theta%3D%5Cfrac%7Bpi%7D%7B2%7D"></picture>

MAC 2311C Lecture 7: 8.2 Area of a sad face of Revolution

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