List of top Mathematics Questions on Calculus asked in MET

If \( f(x) = \begin{cases} x^3 - 3x^2 - 12x + 1, & -1 \le x \le 2 \\ 37 - 2x, & 2 < x \le 3 \end{cases} \), then

$\lim_{n \to \infty} \left[ \frac{1}{n+1} + \frac{1}{n+2} + \frac{1}{n+3} + \ldots + \frac{1}{n+6n} \right]$ is

$\int_{-1/2}^{1/2} \frac{dx}{\sqrt{1-x^2}}$ is equal to

$\int_0^1 x^{12} (1-x)^{10} dx$ is equal to

If $f(x+y) = f(x) \cdot f(y)$, $f(3) = 3$, $f'(0) = 11$, then $f'(3)$ is equal to

$\frac{d}{dx} \left[ \int_0^{x^2} \sin^{-1} \left( \frac{1}{1+t} \right) dt \right]$ is equal to

The area bounded by the curve $y = 4x^3 - 3x^2 + 2x + 3$ with x-axis and ordinates corresponding to the minima of y is

$\int \log_e (a^x + x^a) dx$ is equal to

$\lim_{n \to \infty} \left( \frac{1}{4n^2 - 1} + \frac{1}{4n^2 - 4} + \frac{1}{4n^2 - 9} + \ldots + \frac{1}{4n^2 - n^2} \right)$ is equal to

$\int \frac{dx}{x^2 + 4x + 13}$ is equal to

If $x = \sin^{-1}(3t - 4t^3)$ and $y = \cos^{-1}(2t - 1)$, then $\frac{dy}{dx}$ is equal to

The area between $y^2 + 4x - 8 = 0$, the x-axis and the line $x = 1$ is

If $f(x) = \frac{\tan(3x)}{x} + \frac{x}{2}$ is continuous at $x = 0$, then $f(0)$ is equal to

$\lim_{x\to 0} \frac{\sin x - \sin x}{x^3}$ is

$\int_0^{2a} \frac{f(x)}{f(x)+f(2a-x)} dx$ is equal to

$\int \frac{\tan x}{\sin x \cos x} dx$ is equal to

The equation of the tangent to the curve $(1+x^2)y = 2 - x$, where it crosses the x-axis, is

$\lim_{x\to 0} \frac{1-\cos mx}{1-\cos nx}$ is equal to

$\int_{-\pi/2}^{\pi/2} |\sin x| dx$ is

The function $y = a(1-\cos x)$ is maximum when x is equal to

\( z = \tan(y + ax) + \sqrt{y - ax} \implies z_{xx} - a^{2} z_{yy} \) is equal to