Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

Evaluate the following definite integrals as limit of sums.

`int_0^4 (x + e^(2x)) dx`

Evaluate the definite integral:

`int_(pi/2)^pi e^x ((1-sinx)/(1-cos x)) dx`

Evaluate the definite integral:

`int_0^(pi/4) (sinx cos x)/(cos^4 x + sin^4 x)`dx

Evaluate the definite integral:

`int_0^(pi/2) (cos^2 x dx)/(cos^2 x + 4 sin^2 x)`

Evaluate the definite integral:

`int_(pi/6)^(pi/3)  (sin x + cosx)/sqrt(sin 2x) dx`

Evaluate the definite integral:

`int_0^1 dx/(sqrt(1+x) - sqrtx)`

Evaluate the definite integral:

`int_0^(pi/4) (sin x +  cos x)/(9+16sin 2x) dx`

Evaluate the definite integral:

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

Evaluate the definite integral:

`int_1^4 [|x - 1|+ |x - 2| + |x -3|]dx`

Prove the following:

`int_1^3 dx/(x^2(x +1)) = 2/3 + log  2/3`

Prove the following:

`int_0^1 xe^x dx = 1`

Prove the following:

`int_(-1)^1 x^17 cos^4 xdx = 0`

Prove the following:

`int_0^(pi/2) sin^3 xdx = 2/3`

Prove the following:

`int_0^(pi/4) 2 tan^3 xdx = 1 - log 2`

Prove the following:

`int_0^1sin^(-1) xdx = pi/2 - 1`

Evaluate  `int_0^1 e^(2-3x) dx` as a limit of a sum.

`int dx/(e^x + e^(-x))` is equal to ______.

`int (cos 2x)/(sin x + cos x)^2dx` is equal to ______.

If f (a + b - x) = f (x), then `int_a^b x f(x )dx` is equal to ______.

Choose the correct answers The value of `int_0^1 tan^(-1)  (2x -1)/(1+x - x^2)` dx is 

(A) 1

(B) 0

(C) –1

(D) `pi/4`