Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

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

Integrate the function in x sec² x.

Integrate the function in tan^-1 x.

Integrate the function in x (log x)².

Integrate the function in (x² + 1) log x.

Integrate the function in e^x (sinx + cosx).

Integrate the function in `(xe^x)/(1+x)^2`.

Integrate the function in `e^x (1 + sin x)/(1+cos x)`.

Integrate the function in `e^x (1/x - 1/x^2)`.

Integrate the function in `((x- 3)e^x)/(x - 1)^3`.

Integrate the function in e^2x sin x.

Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.

`intx^2 e^(x^3) dx` equals: 

`int e^x sec x (1 +   tan x) dx` equals:

Find the area of a parallelogram whose adjacent sides are represented by the vectors\[2 \hat{i} - 3 \hat{k} \text { and } 4 \hat{j} + 2 \hat{k} .\]

Find : 

`∫(log x)^2 dx`

If x^y - y^x = a^b, find `(dy)/(dx)`.

If `"x" = "e"^(cos2"t")  "and"  "y" = "e"^(sin2"t")`, prove that `(d"y")/(d"x") = - ("y"log"x")/("x"log"y")`.

If x^y = e^x–y, prove that `("d"y)/("d"x) = logx/(1 + logx)^2`

The derivative of log₁₀x w.r.t. x is ______.