List of top Mathematics Questions on Calculus asked in Kerala Plus Two(Class 12)

Evaluate $\displaystyle \int \frac{dx}{\sqrt{x^2 + 2x + 2}}$.
Solve the differential equation $\displaystyle \frac{dy}{dx} + \frac{y}{x} = x^2$.
Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1$, $x = 4$ and the $x$-axis.
Prove that the function $f(x) = |x|$ is continuous but not differentiable at $x = 0$.