Integration by Parts
Posted: Tue Mar 07, 2017 12:31 am
Integration by Parts is a method of integration, often useful when an integrand can be expressed as a multiplication of two functions.
The method uses the formula
, where are the two functions.
Example
Evaluate the following integral
Solution
We apply the formula , where
From , we have . To find out why this is true:
,
Differentiating both sides,
(you can make subject and then take derivative)
.
Now,
, where is constant.
Simplifying, we get
.
Any question/comment?
The method uses the formula
, where are the two functions.
Example
Evaluate the following integral
Solution
We apply the formula , where
From , we have . To find out why this is true:
,
Differentiating both sides,
(you can make subject and then take derivative)
.
Now,
, where is constant.
Simplifying, we get
.
Any question/comment?