HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions

Evaluate : `∫(x+1)/((x+2)(x+3))dx`

Evaluate : `∫1/(3+2sinx+cosx)dx`

Evaluate: `int 1/(x(x-1)) dx`

Prove that:

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

Solve:

dy/dx = cos(x + y)

Evaluate `int 1/(3+ 2 sinx + cosx) dx`

`int "dx"/(9"x"^2 + 1)= ______. `

Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`

 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`