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

If y = 500e^7x + 600e^–7x, show that `(d^2y)/(dx^2)` = 49y.

If e^y (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.

If y = (tan^–1 x)², show that (x² + 1)² y₂ + 2x (x² + 1) y₁ = 2

Evaluate the definite integral:

`int_(-1)^1 (x + 1)dx`

Evaluate the definite integral:

`int_2^3 1/x dx`

Evaluate the definite integral:

`int_1^2 (4x^3 - 5x^2 + 6x + 9)  dx`

Evaluate the definite integral:

`int_0^(pi/4) sin2xdx`

Evaluate the definite integral:

`int_0^(pi/2) cos 2x  dx`

Evaluate the definite integral:

`int_4^5 e^x dx`

Evaluate the definite integral:

`int_0^(pi/4) tan x dx`

Evaluate the definite integral:

`int_(pi/6)^(pi/4) cosec x  dx`

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`