Arts (English Medium) इयत्ता १२ - CBSE Important Questions

Find the following integrals:

`int (x^3 - x^2 + x - 1)/(x - 1) dx`

Evaluate the definite integral:

`int_0^(pi/2) cos^2 xdx`

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/4) log (1+ tan x) dx`

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`

Find `int (cos theta)/((4 + sin^2 theta)(5 - 4 cos^2 theta)) d theta`

Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`

Find `int dx/(5 - 8x - x^2)`

Find `int(e^x dx)/((e^x - 1)^2 (e^x + 2))`

Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`

Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx

Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`

Evaluate the following integral:

Evaluate each of the following integral:

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

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

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

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

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

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