   Chapter 4.R, Problem 23E

Chapter
Section
Textbook Problem

# Evaluate the integral, if it exists. ∫ − π / 4 π / 4 t 4 tan t 2 + cos t   d t

To determine

To evaluate:

-π/4π/4t4 tant2+cost dt if it exists

Explanation

1) Concept:

By using theorem for integration of an odd function

2) Theorem:

Suppose f is continuous on [-a, a] and if f is odd [f-x=-fx], then

-aaf(x)dx=0

3) Given:

-π/4π/4t4 tant2+cost dt

4) Calculation:

Consider,

-π/4π/4t4 tant2+cost dt

Here,

ft=t4 tant2+cost

Now,

f-t=(-t)4tan(

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