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

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)`

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

`int_(-5)^5 | x + 2| dx`

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

`int_2^8 |x - 5| dx`

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

`int_0^1 x(1-x)^n dx`

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

`int_0^(pi/4) log (1+ tan x) dx`

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

`int_0^2 xsqrt(2 -x)dx`

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

`int_0^(pi/2) (2log sin x - log sin 2x)dx`

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

`int_((-pi)/2)^(pi/2) sin^2 x  dx`

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

`int_0^pi (x  dx)/(1+ sin x)`

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

`int_(pi/2)^(pi/2) sin^7 x dx`