   Chapter 4.5, Problem 4E

Chapter
Section
Textbook Problem

# Evaluate the integral by making the given substitution. ∫ sin 2 θ cos θ   d θ ,   u=sin θ

To determine

To evaluate:

The integral sin2θcosθ dθ by making the given substitution u=sinθ.

Explanation

1) Concept:

i) The substitution rule

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

ii) Indefinite integral:

xn dx=xn+1n+1+C   (n-1)

2) Given:

sin2θcosθ dθ     u=sinθ

3) Calculation:

Use the substitution u=sinθ.

Differentiate u=sinθ with respect to θ.

du=cosθdθ,

By using concept i)

Substitute u=sinθ,cosθdθ=du

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