List of top Mathematics Questions on Evaluation of Definite Integrals by Substitution asked in CBSE CLASS XII

Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).
Evaluate \( \int_{0}^{\pi/4} \frac{x}{1+\cos 2x + \sin 2x} \, dx \).
(b) If \(y = (\tan x)^x\), then find \(\frac{dy}{dx}\).
(a) If \(\sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y)\), prove that \(\frac{dy}{dx} = \sqrt{\frac{1 - y^2}{1 - x^2}}\).
Find the absolute maximum and minimum values of the function: \[ f(x) = 12x^{4/3} - 6x^{1/3}, \quad x \in [0, 1]. \]
The number of points, where \( f(x) = \lfloor x \rfloor \), \( 0 < x < 3 \) (\(\lfloor \cdot \rfloor\) denotes the greatest integer function), is not differentiable is: