List of top Mathematics Questions on Calculus asked in JEE Main

Let P(x) be a real polynomial of degree 3 which vanishes at x = -3. Let P(x) have local minima at x = 1, local maxima at x = -1 and ∫_{-1}^{1} P(x) dx = 18, then the sum of all the coefficients of the polynomial P(x) is equal to ________.
Let f: R → R satisfy the equation f(x + y) = f(x) · f(y) for all x, y ∈ R and f(x) ≠ 0 for any x ∈ R. If the function f is differentiable at x=0 and f'(0)=3, then lim_{h → 0} (1/h) (f(h) - 1) is equal to ________.
The value of the definite integral $\int_{\pi/24}^{5\pi/24} \frac{dx}{1 + \sqrt[3]{\tan 2x}}$ is :
Let f(x) and g(x) be two functions satisfying f(x²) + g(4-x) = 4x³ and g(4-x) + g(x) = 0, then the value of ∫$_{-4}^{4}$ f(x²) dx is __________.
The value of the integral, ∫ from 1 to 3 of [x² - 2x - 2] dx, where [x] denotes the greatest integer less than or equal to x, is :
Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2-x) for all x ∈ (0, 2), f(0) = 1 and f(2) = e². Then the value of ∫ from 0 to 2 f(x) dx is :
The area of the region : R = {(x, y) : 5x² ≤ y ≤ 2x² + 9} is :