   Chapter 4.R, Problem 31E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C=0). ∫ cos x 1 + sin x   d x

To determine

To evaluate:

cosx1+sinxdx   and verify using graphing function

Explanation

1) Concept:

i) Indefinite integration:

fx=F(x) if F'x=f(x)

ii) The Substitution rule:

If u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then

fgxg'(x) dx=f(u)du

2) Formula:

xndx=xn+1n+1+C

3) Given:

cosx1+sinxdx

4) Calculation:

Substitute, u=1+sinx

Differentiating with respect to x,

dudx=cosx

du=cosx dx

cosx1+sinxdx=duu=u-12 du

By using formula,

u-12 du

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