Evaluate the following definite Integral: ∫x^2 cos x dx, x ∈[0, π/2 ]

Question

Evaluate the following definite Integral:

\(\int\limits_0^{\pi/2} \)x²cos x dx

Answer 1

For this, we have to apply integration by parts

Let u and v be two functions then

\(\int\)udv = uv - \(\int\)vdu

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.

So now we have to substitute the limits in this equation.

And should subtract upper limit value from lower limit value