Commerce (English Medium) इयत्ता १२ - 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:

For the curve y = 5x – 2x³, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3

Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by  x² - y² = cx

Find the equations of the tangent and the normal, to the curve 16x² + 9y² = 145 at the point (x₁, y₁), where x₁ = 2 and y₁ > 0.

If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`