Homework 11 Solution - Integration by Parts SUGGESTED REFERENCE MATERIAL As you work through the problems listed below you should reference Chapter 7.2

# Homework 11 Solution - Integration by Parts SUGGESTED...

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Integration by Parts SUGGESTED REFERENCE MATERIAL: As you work through the problems listed below, you should reference Chapter 7.2 of the rec- ommended textbook (or the equivalent chapter in your alternative textbook/online resource) and your lecture notes. EXPECTED SKILLS: Be able to use integration by parts to evaluate various integrals, including integrands in- volving products of functions, isolated logarithmic functions, or isolated inverse trigono- metric functions. PRACTICE PROBLEMS: For problems 1-12, evaluate the given integral. 1. Z xe 4 x dx x 4 e 4 x - 1 16 e 4 x + C 2. Z x 2 cos ( x ) dx x 2 sin x + 2 x cos x - 2 sin x + C 3. Z x 2 ln ( x ) dx 1 3 x 3 ln x - 1 9 x 3 + C 4. Z ln x x 4 dx - 1 3 x - 3 ln x - 1 9 x - 3 + C 5. Z arcsin ( x ) dx x arcsin x + 1 - x 2 + C 6. Z x sec 2 ( x ) dx x tan x + ln | cos x | + C 1
13. Suppose thatuandvare differentiable functions ofxwithZ10v du= 3 and the fol-lowing functional values.xu(x)v(x)05217-4Use this information to compute