Answered: How should we choose u and du? Hint: we…

How should we choose u and du? Hint: we can write the integral as /1- sin-'z dz 1 sin-x in which case du 1-x dv =1 1 in which case v=x

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Where did I go wrong in the highlighted red box? What is the correct solution

Integration by Parts - Indefinite Integral
Let u = f(x) and v = g(x) be functions with continuous derivatives. Then, the integration-by-parts formula for the integral involving these two functions is:
%3!
= uv -
In the following problem, we will use integration-by-parts to evaluate the indefinite integral
sin-1z de
Part 1.
How should we choose u and du?
Hint: we can write the integral as /
1. sin-z dz
1
sin-x in which case du
1-x
dv = 1 in which case v = x
Note: omit the arbitrary constant in your answer for v. To see why this is acceptable, check out example 3.1 from the text.
Part 2.
Use the integration-by-parts formula to re-write the integral
1
sin
z dz
x sin-x
V1-x
Part 3.
Finally, evaluate the indefinite integral.
sinz dr
x sin
x+ V1-x + C
Your answer here should contain an arbitrary constant.

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