Science (English Medium) कक्षा १२ - CBSE Important Questions for Mathematics

Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(cosx))dx`

Find:

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

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`

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

Evaluate `int_(-2)^2x^2/(1+5^x)dx`

Evaluate `int_(-1)^2(e^3x+7x-5)dx` as a limit of sums

Evaluate:

`int x^2/(x^4+x^2-2)dx`

Evaluate:

`int((x+3)e^x)/((x+5)^3)dx`

Find the particular solution of the differential equation x²dy = (2xy + y²) dx, given that y = 1 when x = 1.

find `∫_2^4 x/(x^2 + 1)dx`

Evaluate :   `∫1/(cos^4x+sin^4x)dx`

Evaluate :

`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`

If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.

Evaluate :

`int_e^(e^2) dx/(xlogx)`

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

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

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`