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What will go wrong if we choose u = x²? Notice: in that case, we will also be choosing du = ln x dx.

What will go wrong if we choose u = x²? Notice: in that case, we will also be choosing du = ln x dx.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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Consider the indefinite integral fx². (In x) dx To use Integration by Parts, we'll apply the formula fu udvu.v- Sv.du. To use this formula, we must decide which factor in the given integrand will play the role of u, and which will play the role of dv. x²? What will go wrong if we choose u = Notice: in that case, we will also be choosing du = ln x dx. We will have trouble when we try to find du, because it's not simple to differentiate u = x². O We will have trouble when we try to find v, because it's not simple to antidifferentiate du = ln x dx. O Nothing will go wrong, because it's simple to find du by differentiating u = x². After we have u and du, we are ready to use the formula. O Nothing will go wrong, because it's simple to find du by differentiating v = ln x.
Transcribed Image Text:Consider the indefinite integral fx². (In x) dx To use Integration by Parts, we'll apply the formula fu udvu.v- Sv.du. To use this formula, we must decide which factor in the given integrand will play the role of u, and which will play the role of dv. x²? What will go wrong if we choose u = Notice: in that case, we will also be choosing du = ln x dx. We will have trouble when we try to find du, because it's not simple to differentiate u = x². O We will have trouble when we try to find v, because it's not simple to antidifferentiate du = ln x dx. O Nothing will go wrong, because it's simple to find du by differentiating u = x². After we have u and du, we are ready to use the formula. O Nothing will go wrong, because it's simple to find du by differentiating v = ln x.
Consider these three examples: A. S -dx 1+x² B. S · cos x dx sin²x C.S.sin x dx We want to solve one using a basic antiderivative, one using u-substitution, and one using integration by parts. Match each problem to the most appropriate technique. A B с [Choose ] [Choose ] basic antiderivative [Choose ] integration by parts basic antiderivative u-substitution
Transcribed Image Text:Consider these three examples: A. S -dx 1+x² B. S · cos x dx sin²x C.S.sin x dx We want to solve one using a basic antiderivative, one using u-substitution, and one using integration by parts. Match each problem to the most appropriate technique. A B с [Choose ] [Choose ] basic antiderivative [Choose ] integration by parts basic antiderivative u-substitution
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