   Chapter 4.5, Problem 1E

Chapter
Section
Textbook Problem

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

To determine

To evaluate:

The integral cos2x dx by making the given substitution u=2x.

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 oninterval I, then f(gx)g'xdx=f(u)du.

ii) Indefinite integral:

cosx dx=-sinx+C

2) Given:

cos2x dx,      u=2x

3) Calculation:

Use substitution,  u=2x

Differentiating u=2x

du=2 dx

Solve for dx by dividing both sideby 2.

dx=du2

By using concept i)

Substitute u=2x and dx=du2 in (1)

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