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MTH 142 Lecture 7: Section 7.1 Integration by Parts

United States

College Calculus 2

Mathematics

Brian Hassard

University at Buffalo

General Physics II

General Physics II Lab

Proof In Exercises 71-76, use integration by parts to prove the formula. (For Exercises 71-74, assume that n is a positive integer.)
<picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/873869252315721/question/0.webp?img=6c76275f8dc480747c024cb381484177" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/873869252315721/question/0.png?img=a77f24a643455efca60eb0fdba7a244a" data-mlang="latex" data-equation="%7Bint%7Bx%5E%7Bn%7Dsinx%7D%7D%2Cdx%3D-x%5E%7Bn%7Dcosx%2Bn%7Bint%7Bx%5E%7Bn-1%7Dcosx%2Cdx%7D%7D"></picture>

Proof In Exercises 71-76, use integration by parts to prove the formula. (For Exercises 71-74, assume that n is a positive integer.)
<picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/882532274811695/question/0.webp?img=a672d7104ebbbc8975adbf451a74bb68" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/882532274811695/question/0.png?img=69cde1cf4ccdc05ee6acedeb6815b567" data-mlang="latex" data-equation="%7Bint%7Bx%5E%7Bn%7Dcosx%7D%7D%2Cdx%3D-x%5E%7Bn%7Dsinx-n%7Bint%7Bx%5E%7Bn-1%7Dsinx%2Cdx%7D%7D"></picture>

Proof In Exercises 71-76, use integration by parts to prove the formula. (For Exercises 71-74, assume that n is a positive integer.)
<picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/437561659089946/question/0.webp?img=648726a9d95b0a1426fcde23e40502d5" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/437561659089946/question/0.png?img=9f031bdccaca1d329437f3e5bd016eb9" data-mlang="latex" data-equation="%7Bint%7Bx%5E%7Bn%7Dlnx%7D%7D%2Cdx%3D%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7B%7B%28n%2B1%29%7D%5E%7B2%7D%7Dlbrack-1%2B%28n%2B1%29lnxrbrack%2BC"></picture>

MTH 142 Lecture 7: Section 7.1 Integration by Parts

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