Q. 314.2( 5 Votes )

Evaluate the following definite Integrals:

Answer :

For this we have to apply integration by parts

Let u and v be two functions then

To choose the first function u we use “ILATE” rule

That is

I=inverse trigonometric function

L=logarithmic function

A=algebraic function

T=trigonometric functions

E=exponential function

So in this preference, the first function is chosen to make the integration simpler.

Now, In the given question x2 is an algebraic function and it is chosen as u(A comes first in “ILATE” rule)

So first let us integrate the equation and then let us substitute the limits in it.

Let us recall a formula cos2x=2–1

Now substitute it

Now let us recall other formula i.e=


Using them we can write the equation as

On substituting these values we get

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Fundamental Integration Formula59 mins
Integration by Substitution56 mins
Interactive Quiz on Integration by Parts56 mins
Interactive Quiz on Integration by Substitution47 mins
Lecture on Integration by parts55 mins
Lecture on some forms of integration54 mins
Lecture on integration by partial fractions62 mins
Definite Integration | Ready for a quiz?FREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses