HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Show that `sin^-1(3/5)  + sin^-1(8/17) = cos^-1(36/85)`

Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`

Find the distance between the parallel lines `x/2 = y/(-1) = z/2` and `(x - 1)/2 = (y - 1)/(-1) = (z - 1)/2`

`int (sinx)/(1 + sin x)  "d"x`

`int 1/(4x + 5x^(-11))  "d"x`

`int (sin(x - "a"))/(cos (x + "b"))  "d"x`

`int 1/sqrt(2x^2 - 5)  "d"x`

`int ["cosec"(logx)][1 - cot(logx)]  "d"x`

`int (cos2x)/(sin^2x cos^2x)  "d"x`

`int sin4x cos3x  "d"x`

`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`

`int sqrt(tanx) + sqrt(cotx)  "d"x`

`int_0^(x/4) sqrt(1 + sin 2x)  "d"x` =

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`