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

The maximum value of sinx + cosx is ______.

At what point, the slope of the curve y = – x³ + 3x² + 9x – 27 is maximum? Also find the maximum slope.

Prove that f(x) = sinx + `sqrt(3)` cosx has maximum value at x = `pi/6`

At x = `(5pi)/6`, f(x) = 2 sin3x + 3 cos3x is ______.

The least value of the function f(x) = `"a"x + "b"/x` (where a > 0, b > 0, x > 0) is ______.

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)