Chapter 4.5, Problem 78E

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

Chapter
Section

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
Textbook Problem

# Using Symmetry Use the symmetry of the graphs of the sine and cosine functions as an aid in evaluating each definite integral.(a). ∫ − π / 4 π / 4 sin x d x (b). ∫ − π / 4 π / 4 cos x d x (c). ∫ − π / 2 π / 2 cos x d x (d). ∫ − π / 2 π / 2 sin x cos x d x

(a)

To determine

To calculate: The value of definite integral π/4π/4sinxdx.

Explanation

Given:

Integral âˆ«âˆ’Ï€/4Ï€/4sinxdx.

Formula used:

If f is an odd function then âˆ«âˆ’aaf(x)dx=0.

As according to fundamental theorem of calculus,

âˆ«abf(x)dx=F(b)âˆ’F(a)

Calculation:

Consider: f(x)=sinx

(b)

To determine

To calculate: The value of definite integral π/4π/4cosxdx.

(c)

To determine

To calculate: The value of definite integral π/2π/2cosxdx.

(d)

To determine

To calculate: The value of definite integral π/2π/2sinxcosxdx.

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