If $\displaystyle\int_0^a \dfrac{dx}{1 + 4x^2} = \dfrac{\pi}{8}$, then $a =$

The value of the integral $\displaystyle\int_{-\sqrt{3}}^{\sqrt{3}} \dfrac{(2x^9 + 3x^8 - 5x^7 + 9x^6 + 4x^3 - x + 3)}{x^2 + 3} \, dx$ is

The area of the region (in sq.units) bounded by the curve $y = 2\sqrt{1 - x^2}$ and the X-axis is _____

If $\dfrac{dy}{dx} = y + 5$ and $y(0) = 4$ then $y(\log 2)$ is equal to