DEFINE INTEGRALS

Example 1 :

Evaluate the following

Solution :

Let t  =  cos x

Differentiating both sides with respect to x

dt  =  -sin x dx and sin x dx  =  -dt

We have changed the given function in terms of t from the variable x .So, we need to change the limits also.

When x  =  0

t  =  cos 0

t  =  1

When x  =  Π/2

t  =  cos Π/2

t  =  0

Example 2 :

Evaluate the following

Integral 0 to Π/2 sin² x

Solution :

To solve this problem we have to use the trigonometric formula for sin² x.

sin²x  =   (1 - cos 2x)/2

Example 3 :

Evaluate the following

Solution :

t  =  Sin⁻¹x

Differentiating with respect to x on both sides

 dt  =  1/√(1-x²) dx

Related Pages

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Representing a Decimal Number

    Apr 01, 23 11:43 AM

    representingdecimalnumbers1
    Representing a Decimal Number

    Read More

  2. Comparing Irrational Numbers Worksheet

    Mar 31, 23 10:41 AM

    tutoring.png
    Comparing Irrational Numbers Worksheet

    Read More

  3. Comparing Irrational Numbers

    Mar 31, 23 10:18 AM

    Comparing Irrational Numbers - Concept - Examples with step by step explanation

    Read More