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=


and


Using them we can write the equation as












On substituting these values we get




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