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
I=inverse trigonometric 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
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