The value of the integral $\int_{-\pi/2}^{\pi/2}\left(\dfrac{x^2 \cos x}{1+e^x}\right)dx$ is equal to $\left(\dfrac{\pi^2}{A}\right) - B$. Then $\left(\dfrac{A}{B}\right) = $

The area of the smaller region bounded by the circle $x^2 + y^2 = 4$ and the line $x = 1$ is...

If the area bounded by the curve $x^2 = by$ and the lines $y = 1, y = 4$ in the first quadrant is $28$ sq. units, then the value of b is...

The solution of the differential equation $\dfrac{dy}{dx} = e^{x-y} + x^2 e^{-y}$ is...