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

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:

`sin xy + x/y` = x² – y

sec(x + y) = xy

tan^–1(x² + y²) = a

(x² + y²)² = xy

If ax² + 2hxy + by² + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1 

If x sin (a + y) + sin a cos (a + y) = 0, prove that `"dy"/"dx" = (sin^2("a" + y))/sin"a"`

If y = tan^–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.

The derivative of cos^–1(2x² – 1) w.r.t. cos^–1x is ______.