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

Find \[ \int \frac{x^2 + 1}{(x^2 + 2)(2x^2 + 1)} \, dx \]
Evaluate: \[ \int_1^5 \left( |x-2| + |x-4| \right) \, dx \]
Evaluate: \( \int_0^1 \frac{2x}{5x^2 + 1} dx \)
\( \int \frac{\cos 2x - \cos 2\theta}{\cos x - \cos \theta} dx \) is equal to:
The area of the region enclosed between the curve \( y = |x| \), x-axis, \( x = -2 \) and \( x = 2 \) is:
Evaluate: \[ \int_1^5 \left( |x-2| + |x-4| \right) \, dx \]
Find: \[ \int \frac{2x}{(x^2 + 3)(x^2 - 5)} \, dx \]
If \( \int_0^a \frac{1}{1 + 4x^2} \, dx = \frac{\pi}{8} \), then the value of \(a\) is:
\( \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx \) is equal to:

Evaluate:
$\displaystyle \int_{0}^{3} x \cos(\pi x) \, dx$

Find:$\displaystyle \int \dfrac{dx}{\sin x + \sin 2x}$

Find: \[ \int \frac{\sqrt{x}}{1 + \sqrt{x^{3/2}}} \, dx \]
If $ \int e^{-3 \log x} \, dx = f(x) + C $, then $ f(x) $ is:
$\int e^x (\cos x - \sin x) \, dx$ is equal to:
Find: \[ \int \frac{\cos x}{(4 + \sin^2 x)(5 - 4 \cos^2 x)} \, dx. \]
Evaluate: \[ \int_0^{\frac{\pi}{2}} \frac{5 \sin x + 3 \cos x}{\sin x + \cos x} \, dx \]
Find: \[ \int \frac{\cos 2x}{(\sin x + \cos x)^2} \, dx \]
Evaluate the integral: \[ \int_{0}^{\frac{\pi}{4}} \sqrt{1 + \sin^2 x} \, dx \]

Evaluate:
\[ I = \int_2^4 \left( |x - 2| + |x - 3| + |x - 4| \right) dx \]

\[ \int \frac{\tan^2 \sqrt{x}}{\sqrt{x}} \, dx \text{ is equal to:} \]
Using integration, find the area of the region
{(x,y) : 0 ≤ y ≤ x2, 0 ≤ y ≤ x, 0 ≤ x≤3}

Find:\[ \int \frac{dx}{(x + 2)(x^2 + 1)} \]

The area bounded by the curve \(x = y^2\), the y-axis, and the lines \(y = 3\) and \(y = 4\) is:
If \(\dfrac{d}{dx}f(x) = 3x^2 - \dfrac{3}{x^4}\), and \(f(1) = 0\), then \(f(x)\) is:
Find: \( \int \frac{5x}{(x + 1)(x^2 + 9)} dx \).