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

Evaluate the following integral:

Evaluate the following integral:

Evaluate : 

Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .

Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .

Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .

Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .

Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x"  d"x"`.

Evaluate:  `int_-1^2 (|"x"|)/"x"d"x"`.

Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.

Find: `int_  (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.

Evaluate the following:

`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`

Evaluate the following:

`int "dt"/sqrt(3"t" - 2"t"^2)`

Find: `int (dx)/sqrt(3 - 2x - x^2)`

Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.

Evaluate `int_(-2)^2x^2/(1+5^x)dx`

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/2) cos^2 x dx`

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/2)  sqrt(sinx)/(sqrt(sinx) + sqrt(cos x)) dx` 

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/2) sin^(3/2)x/(sin^(3/2)x + cos^(3/2) x) dx`

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/2)  (cos^5  xdx)/(sin^5 x + cos^5 x)`