Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Evaluate the integral by using substitution.

`int_0^(pi/2) sqrt(sin phi) cos^5 phidphi`

Evaluate the integral by using substitution.

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

Evaluate the integral by using substitution.

`int_0^2 xsqrt(x+2)`  (Put x + 2 = `t^2`)

Evaluate the integral by using substitution.

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

Evaluate the integral by using substitution.

`int_0^2 dx/(x + 4 - x^2)`

Evaluate the integral by using substitution.

`int_(-1)^1 dx/(x^2 + 2x  + 5)`

Evaluate the integral by using substitution.

`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`

The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.

If `f(x) = int_0^pi t sin  t  dt`, then f' (x) is ______.

Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`

Evaluate of the following integral:

(i)  \[\int x^4 dx\]

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