Arts (English Medium) Class 12 - CBSE Important Questions

Evaluate : \[\int\limits_0^\pi/4 \frac{\sin x + \cos x}{16 + 9 \sin 2x}dx\] .

Evaluate : \[\int\limits_0^{2\pi} \cos^5 x dx\] .

Find : \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\] .

Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .

Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .

Find :  \[\int\frac{e^x}{\left( 2 + e^x \right)\left( 4 + e^{2x} \right)}dx.\] 

Evaluate : \[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\] .

Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .

Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .

Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .

Evaluate: \[\int\limits_{- \pi/2}^{\pi/2} \frac{\cos x}{1 + e^x}dx\] .

Evaluate : \[\int e^{2x} \cdot \sin \left( 3x + 1 \right) dx\] .

Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .

Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .

Evaluate : \[\int\frac{dx}{\sin^2 x \cos^2 x}\] .

Evaluate : \[\int\limits_0^\frac{\pi}{4} \tan x dx\] .

Evaluate : \[\int\frac{x \cos^{- 1} x}{\sqrt{1 - x^2}}dx\] .

Evaluate : \[\int(3x - 2) \sqrt{x^2 + x + 1}dx\] .

Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x + \tan x}dx\] .