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

Evaluate the definite integral:

`int_0^1 dx/sqrt(1-x^2)`

Evaluate the definite integral:

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

Evaluate the definite integral:

`int_2^3 dx/(x^2 - 1)`

Evaluate the definite integral:

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

Evaluate the definite integral:

`int_2^3 (xdx)/(x^2 + 1)`

Evaluate the definite integral:

`int_0^1 (2x + 3)/(5x^2 + 1) dx`

Evaluate the definite integral:

`int_0^1 x e^(x^2) dx`

Evaluate the definite integral:

`int_1^2 (5x^2)/(x^2 + 4x + 3)`

Evaluate the definite integral:

`int_0^(pi/4) (2 sec^2 x + x^3  + 2) dx`

Evaluate the definite integral:

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

Evaluate the definite integral:

`int_0^2 (6x +3)/(x^2 + 4)` dx

Evaluate the definite integral:

`int_0^1 (xe^x + sin  (pix)/4)`

`int_1^(sqrt3)dx/(1+x^2) ` equals:

`int_0^(2/3) dx/(4+9x^2)` equals:

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

Find `("d"^2"y")/"dx"^2`, if y = `"x"^-7`

`sin xy + x/y` = x² – y

sec(x + y) = xy

tan^–1(x² + y²) = a

(x² + y²)² = xy