Chapter 5: Q. 4 (page 494)

Fill in the blanks to complete each of the following theorem statements:
If $u = u (x)$ and $v = v (x)$ are differentiable functions, then the following integration-by-parts formula holds: $\int u d v =_-_.$

Short Answer

Expert verified

If $u = u (x)$ and $v = v (x)$ are differentiable functions, then the following integration-by-parts formula holds: $\int u d v = u v - \int v d u .$

Step by step solution

Step 1. Given information

If $u = u (x)$ and $v = v (x)$ are differentiable functions, then the following integration-by-parts formula holds: $\int u d v =_____-_____.$

Step 2. Filling in the blanks to complete the theorem statements

If $u = u (x)$ and $v = v (x)$ are differentiable functions, then the following integration-by-parts formula holds: $\int u d v = u v - \int v d u .$

This is the standard integration-by-parts formula.

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Fill in the blanks to complete each of the following theorem statements:
If $u = u (x)$ and $v = v (x)$ are differentiable functions, then the following integration-by-parts formula holds: $\int u d v =_-_.$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Filling in the blanks to complete the theorem statements

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Fill in the blanks to complete each of the following theorem statements:If u=u(x)andv=v(x)are differentiable functions, then the following integration-by-parts formula holds:∫udv=_____-_____.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Filling in the blanks to complete the theorem statements

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

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Geometry

Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following theorem statements:
If $u = u (x)$ and $v = v (x)$ are differentiable functions, then the following integration-by-parts formula holds: $\int u d v =_-_.$