   Chapter 8, Problem 51RE

Chapter
Section
Textbook Problem

Integration by Tables In Exercises 49–56, use integration tables to find or evaluate the integral. ∫ 0 π / 2 x 1 + sin x 2 d x

To determine

To calculate: The integral 0π2x1+sinx2dx from the integration table.

Explanation

Given:

The provided integral is:

0π2x1+sinx2dx

Formula used:

From the table of integration formula:

11+sinudu=tanusecu+c

Where, c is the constant of integration.

Calculation:

Start with the provided integral. That is,

0π2x1+sinx2dx

Put x2=t, now differentiate on both sides.

So,

2xdx=dtxdx=dt2

As the dummy variable x is changed to t so the limits of integration will also change.

As, x2=t

So, if x varies from 0 to π2 then value of t varies from 0 to π4.

Write x in the form of t, Put value of xdx in the provided integral and also change the limits according to the new dummy variable t

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