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

Solve the differential equation: x dy - y dx = `sqrt(x^2 + y^2)dx,` given that y = 0 when x = 1.

The product of any matrix by the scalar ______ is the null matrix.

Evaluate `int tan^8 x sec^4 x"d"x`

Find `int "dx"/(2sin^2x + 5cos^2x)`

Find `int x^2tan^-1x"d"x`

`int "e"^x (cosx - sinx)"d"x` is equal to ______.

`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` = ______.

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`.