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

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

Find an anti derivative (or integral) of the following function by the method of inspection.

sin 2x

Find an anti derivative (or integral) of the following function by the method of inspection.

Cos 3x

Find an anti derivative (or integral) of the following function by the method of inspection.

e^2x

Find an anti derivative (or integral) of the following function by the method of inspection.

(axe + b)²

Find an antiderivative (or integral) of the following function by the method of inspection.

sin 2x – 4 e^3x

Find the following integrals:

`int (4e^(3x) + 1)`

Find the following integrals:

`intx^2 (1 - 1/x^2)dx`

Find the following integrals:

`int (ax^2 + bx + c) dx`

Find the following integrals:

`int(2x^2 + e^x)dx`

Find the following integrals:

`int(sqrtx - 1/sqrtx)^2 dx`

Find the following integrals:

`int (x^3 + 5x^2   -4)/x^2 dx`

Find the following integrals:

`int (x^3 + 3x + 4)/sqrtx dx`

Find the following integrals:

`int (x^3 - x^2 + x - 1)/(x - 1) dx`

Find the following integrals:

`int(1 - x) sqrtx dx`

Find the following integrals:

`intsqrtx( 3x^2 + 2x + 3) dx`

Find the following integrals:

`int(2x - 3cos x + e^x) dx`

Find the following integrals:

`int(2x^2 - 3sinx + 5sqrtx) dx`

Find the following integrals:

`intsec x (sec x + tan x) dx`

Find the following integrals:

`int(sec^2x)/(cosec^2x) dx`