   Chapter 8.3, Problem 61E

Chapter
Section
Textbook Problem

# Evaluating a Definite Integral In Exercises 59-66, evaluate the definite integral. ∫ 0 π / 2 cot t 1 + sin t   d t

To determine

To calculate: The value of the integral function, 0π2cott1+sintdt.

Explanation

Given:

The integral function is 0π2cott1+sintdt.

Formula used:

Integration formula, 1udu=lnu+c.

Calculation:

Consider the integral,

0π2cott1+sintdt

The equation is written as,

0π2cott1+sintdt=0π2costsint(1+sint)dt

Substitute, u=1+sint and differentiate both side with respect to t,

du=costdt

Again, the equation is written as,

0π2costsint(1+sint)dt=021u(u

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