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

Differentiate the function with respect to x:

`(sin x - cos x)^((sin x - cos x)), pi/4 < x < (3pi)/4`

Find `dy/dx`, if y = `sin^-1 x + sin^-1 sqrt (1 - x^2)`, 0 < x < 1.

If `xsqrt(1+y) + y  sqrt(1+x) = 0`, for, −1 < x < 1, prove that `dy/dx = -1/(1+ x)^2`.

Find the unit vector in the direction of the vector `veca = hati + hatj + 2hatk`.

Find the unit vector in the direction of vector `vec(PQ)`, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Integrate the function `(3x^2)/(x^6 + 1)`

Integrate the function `1/sqrt(1+4x^2)`

Integrate the function `1/sqrt((2-x)^2 + 1)`

Integrate the function `1/sqrt(9 - 25x^2)`

Integrate the function `(3x)/(1+ 2x^4)`

Integrate the function `x^2/(1 - x^6)`

Integrate the function `(x - 1)/sqrt(x^2 - 1)`

Integrate the function `x^2/sqrt(x^6 + a^6)`

Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`

Integrate the function `1/sqrt(x^2 +2x + 2)`

Integrate the function `1/(9x^2 + 6x + 5)`

Integrate the function `1/sqrt(7 - 6x - x^2)`

Integrate the function `1/sqrt((x -1)(x - 2))`

Integrate the function `1/sqrt(8+3x  - x^2)`

Integrate the function `1/sqrt((x - a)(x - b))`