Evaluate the following integral: ∫{sin^2(3π + x)+ (π + x)^3}dx, x ∈ [-3π /2, -π /2]

Question

Evaluate the following integral:

\(\int\limits_{-3\pi/2}^{-\pi/2} \){sin²(3π  + x)+ (π  + x)³}dx

Answer 1

Let us assume that

I = \(\int\limits_{-3\pi/2}^{-\pi/2} \){sin²(3π  + x)+ (π  + x)³}dx

We know

We know

b and a being the upper and lower limits respectively.

thus

Thus solving the above equation, we get