Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Integrate the function:

`sinx/(sin (x - a))`

Integrate the function:

`(e^(5log x) -  e^(4log x))/(e^(3log x) - e^(2log x))`

Integrate the function:

`cos x/sqrt(4 - sin^2 x)`

Integrate the function:

`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`

Integrate the function:

`1/(cos (x+a) cos(x+b))`

Integrate the function:

`x^3/(sqrt(1-x^8)`

Integrate the function:

`e^x/((1+e^x)(2+e^x))`

Integrate the function:

`1/((x^2 + 1)(x^2 + 4))`

Integrate the function:

`cos^3 xe^(log sinx)`

Integrate the function:

`e^(3log x) (x^4 + 1)^(-1)`

Integrate the function:

f' (ax + b) [f (ax + b)]ⁿ

Integrate the function:

`1/sqrt(sin^3 x sin(x + alpha))`

Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`

Integrate the function:

`sqrt((1-sqrtx)/(1+sqrtx))`

Integrate the function:

`(2+ sin 2x)/(1+ cos 2x) e^x`

Integrate the function:

`(x^2 + x + 1)/((x + 1)^2 (x + 2))`

Integrate the function:

`tan^(-1) sqrt((1-x)/(1+x))`

Integrate the function:

`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`

If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.

The volume of a sphere is increasing at the rate of 8 cm³/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.