| |
|
|
| |
 |
| Some Special Types of Integrals (Contd…) |
 |
| Example: |
| |
Evaluate the integral  |
| |
| Suggested answer: |
| |
| Referring to the above procedure (ii), we have |
| |
 |
| |
 |
| |
| Comparing the coefficients of x and |
| |
| 4A = 1 B = 1 |
| |
B = 1 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
| Put (2x2 + 3) = t |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
| Substituting I1 and I2 from (2) and (3) respectively in (1) we have |
| |
 |
| |
 |
| |
| Method: |
| |
| Taking 1 as the second function and integrating by parts, we get |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
| |
 |
| |
| Method: |
| |
| We make the substitution |
| |
 |
| |
 |
| |
(1+t2)dx 2dt |
| |
|
| |
 |
| |
|
| |
| Similarly, |
| |
 |
| |
 |
| |
By making the above substitutions the integrals will be reduced to the
form which can be integrated by method of completing squares. |
| |
| Example: |
| |
 |
| |
| Suggested answer: |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
| dt = dZ |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
|
|
|
| |
|
|
| |
|
|
|
|
|
(100% money-back guarantee)
Customer Care
Click to get customer service, technical support and subscription help.
Refer-A-Friend
Get One Month Free!
When you refer a friend
|
|
|