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

Find : \( \int \frac{dx}{x^{1/2} + x^{1/3}} \)
Find \( \int \sqrt{\frac{x + 2}{x - 2}} dx \)
Find: \[ \int \frac{\cos x}{(2+\sin x)(4+\sin x)}\,dx. \]
Find : \( \int \frac{dx}{x^{1/2} + x^{1/3}} \)
The indefinite integral $\int \frac{1}{1 + \cos x} \, dx$ is equal to:
The integral \[ \int \sqrt{1 + \sin x} \, dx \] is equal to:
The integral \[ \int_0^{\frac{\pi}{2}} \cos x \cdot e^{\sin x} \, dx \] is equal to:
The integrating factor of the differential equation \[ e^{-\frac{2x}{\sqrt{x}}} \, \frac{dy}{dx} = 1 \] is:
Sketch a graph of \( y = x^2 \). Using integration, find the area of the region bounded by \( y = 9 \), \( x = 0 \), and \( y = x^2 \).

Evaluate: \[ \int_1^5 \left( |x-2| + |x-4| \right) \, dx \]