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

Find `int_  (log "x")^2 d"x"`

Find `int_  (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`

Show that the height of a cylinder, which is open at the top, having a given surface area and greatest volume, is equal to the radius of its base. 

Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration. 

Find: `int_  (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`

Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`

Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`

Find: `int sin^-1 (2x) dx.`

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.

f(x) = x^x has a stationary point at ______.

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`