List of top Mathematics Questions on Integration asked in CBSE CLASS XII, CBSE Compartment XII

If \( \int \frac{1}{2x^2} \, dx = k \cdot 2x + C \), then \( k \) is equal to:

Find: \[ \int \frac{\cos x \, dx}{1 + \cos x + \sin x}. \]

Evaluate: \[ \int_{\frac{\pi}{2}}^{\pi} \frac{e^{x} \left(1 - \sin x \right)}{1 - \cos x} \, dx. \]

If \( \int_0^1 \frac{e^x}{1+x} \, dx = \alpha \), then \( \int_0^1 \frac{e^x}{(1+x)^2} \, dx \) is equal to:

The value of \[ \int_0^1 \frac{dx}{e^x + e^{-x}} \] is :

Find: \[ \int \frac{\sin^{-1} \left( \frac{x}{\sqrt{a + x}} \right)}{ \sqrt{a + x}} \, dx \]

The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:

Evaluate \( \int_0^{\frac{\pi}{2}} \frac{x}{\cos x + \sin x} \, dx \)

Evaluate the integral: \[ \int_{-1}^{1} \frac{|x|}{x} dx, \, x \neq 0 \]

The area of the shaded region bounded by the curves \( y^2 = x, x = 4 \) and the x-axis is given by:

$\int \frac{e^{\log x}}{e^{6 \log x} - e^{5 \log x}} dx$ is equal to:

$\int \frac{e^x}{\sqrt{4 - 2x}} dx$ is equal to:

\[ \int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} \, dx \] is equal to :

The area of the region enclosed by the curve $y = \sqrt{x}$ and the lines $x = 0$ and $x = 4$ and the x-axis is :

The integral \( \int \frac{dx}{\sin^2 x \cos^2 x} \) is equal to

Find \( \int \frac{3x + 1}{(x - 2)^2 (x + 2)} \, dx \)

(a) Find \[ \int \frac{x}{(x - 1)(x^2 + 4)} \, dx \]

\[ \int \frac{a^x}{\sqrt{1 - a^2 x}} \, dx \] is equal to :

\[ \int \frac{e^{9 \log x} - e^{8 \log x}}{e^{6 \log x}} \, dx \] is equal to :

Using integration, find the area of the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad \text{bounded between the lines} \quad x = -\frac{a}{2} \quad \text{to} \quad x = \frac{a}{2}. \]

Evaluate \[ I = \int_0^\pi \frac{x \, \tan x}{\sec x + \tan x} \, dx \]