The value of $\int_{-\pi}^{\pi}\dfrac{2x(1 + \sin x)}{1 + \cos^2 x}dx$ is...

The area of the region enclosed by the lines $y = 2x, 2y = x$ and $x = 2$ (in sq.units) is...

The area of the region common to the parabolas $4y^2 = 9x$ and $3x^2 = 16y$ is...

For the differential equation $\dfrac{d^3y}{dx^3} + \cos\left(\dfrac{d^2y}{dx^2}\right) = 0$, which of the following is true ?