HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

 Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log  |"x" +sqrt("x"^2 +"a"^2) | + "c"`

 Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`

Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`

Evaluate the following integrals:

`int(2)/(sqrt(x) - sqrt(x + 3)).dx`

Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`

Integrate the following function w.r.t. x:

x⁹.sec²(x¹⁰)

Integrate the following functions w.r.t.x:

`(2sinx cosx)/(3cos^2x + 4sin^2 x)`

Integrate the following functions w.r.t.x:

cos⁸xcotx

Evaluate the following:

`int (1)/(25 - 9x^2)*dx`

Evaluate the following : `int sinx/(sin 3x).dx`

Evaluate the following integrals:

`int (7x + 3)/sqrt(3 + 2x - x^2).dx`

Evaluate the following:

`int x^2 sin 3x  dx`

Evaluate the following : `int x^3.logx.dx`

Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`

Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`

`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________

If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______

`int  ("e"^x(x - 1))/(x^2)  "d"x` = ______ 

`int sqrt(1 + sin2x)  dx`

`int cos^7 x  "d"x`