Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

`int "dx"/(sin^2x cos^2x)` is equal to ______.

`int (sin^6x)/(cos^8x) "d"x` = ______.

Evaluate the following:

`int ((1 + cosx))/(x + sinx) "d"x`

Evaluate the following:

`int ("d"x)/(1 + cos x)`

Evaluate the following:

`int tan^2x sec^4 x"d"x`

Evaluate the following:

`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`

Evaluate the following:

`int sqrt(1 + sinx)"d"x`

Evaluate the following:

`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`

Evaluate the following:

`int (cosx - cos2x)/(1 - cosx) "d"x`

Evaluate the following:

`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`

Evaluate the following:

`int sin^-1 sqrt(x/("a" + x)) "d"x`  (Hint: Put x = a tan²θ)

`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.

`int sinx/(3 + 4cos^2x) "d"x` = ______.

If `5 sin theta = 3  "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.

The period of the function f(x) = cos4x + tan3x is ____________.

The general solution of the equation `"cot"  theta - "tan"  theta = "sec"  theta` is ____________ where `(n in I).`

Find the equation of a curve passing through `(1, pi/4)` if the slope of the tangent to the curve at any point P(x, y) is `y/x - cos^2  y/x`.

State the type of the differential equation for the equation. xdy – ydx = `sqrt(x^2 + y^2)  "d"x` and solve it

Which of the following is not a homogeneous function of x and y.

F(x, y) = `(sqrt(x^2 + y^2) + y)/x` is a homogeneous function of degree ______.