Mathematics → Subject Test → Integration by Parts
First of all, why Integration by Parts?
As we know that
But what’s the integration of
So, we use integration by parts technique for the integration of product of functions ( x and cosx in product form ).
Formula for Integration by Parts
Suppose two functions u and v are in product form, then formula for finding their integration is
We can also remember the short formula for Integration by Parts which is usually without dx
Practice Problems
Example 1. Evaluate
Solution
Here,
u = x ⇒ u’ = 1
v = cosx ⇒
Now using Integration by Parts formula
We have,
Answer
Example 2. Evaluate
Solution
Here,
u = 2x2 ⇒ u’ = 4x
v = sinx ⇒
Now using Integration by Parts formula
We have,
The later is again product of functions, and we have to use Integration by parts again. In the example above we have already found that, so using result from the above, we have
Answer
NOTE: 4c and c both are constants, so ignore 4.