HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

If `int_0^1 ("d"x)/(sqrt(1 + x) - sqrt(x)) = "k"/3`, then k is equal to ______.

`int_(pi/5)^((3pi)/10)  sinx/(sinx + cosx)  "d"x` =

`int_0^1 (x^2 - 2)/(x^2 + 1)  "d"x` =

Let I₁ = `int_"e"^("e"^2)  1/logx  "d"x` and I₂ = `int_1^2 ("e"^x)/x  "d"x` then 

`int_0^4 1/sqrt(4x - x^2)  "d"x` =

`int_0^(pi/2) log(tanx)  "d"x` =

Evaluate: `int_(pi/6)^(pi/3) cosx  "d"x`

Evaluate: `int_(- pi/4)^(pi/4) x^3 sin^4x  "d"x`

Evaluate: `int_0^1 1/(1 + x^2)  "d"x`

Evaluate: `int_0^(pi/4) sec^2 x  "d"x`

Evaluate: `int_0^1 |x|  "d"x`

Evaluate: `int_0^1 1/sqrt(1 - x^2)  "d"x`

Evaluate: `int_1^2 x/(1 + x^2)  "d"x`

Evaluate: `int_0^1 "e"^x/sqrt("e"^x - 1)  "d"x`

Evaluate: `int_0^(pi/2)  (sin2x)/(1 +  sin^2x)  "d"x`

Evaluate: `int_0^1(x + 1)^2  "d"x`

Evaluate: `int_(pi/6)^(pi/3) sin^2 x  "d"x`

Evaluate: `int_0^(pi/2) sqrt(1 - cos 4x)  "d"x`

Evaluate:

`int_0^(pi/2) cos^3x  dx`

Evaluate: `int_0^pi cos^2 x  "d"x`