# Integration with Trigonometric Functions

Calculus Level 3

Given $$\displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \frac{b\pi^2}{c}$$, where $$a, b$$ and $$c$$ are positive integers and $$b$$ and $$c$$ are coprime, what is the value of $$a + b + c$$?

×