List of top Mathematics Questions on Calculus asked in MHT CET

Evaluate the integral: \(\int \frac{x}{x + 2} \, dx\).

If \(\tan^{-1}(-1) + \tan^{-1}(5) + \tan^{-1}(3) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\), find \(\alpha\).

Evaluate the integral: \(\int \frac{2x}{x^2 - 5x + 4} \, dx\)

Find the eigenvalues of the matrix \(A = \begin{pmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{pmatrix}\).

Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).

Find the approximate value of \(\sqrt[3]{63}\).

Evaluate: \(\int_0^3 \sqrt{9 - x^2} \, dx\).

The equation \(x^2 - Ky^2 - 4x + 6y - 5 = 0\) represents a pair of straight lines. Find the point of intersection.