HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Important Questions

Evaluate :`intxlogxdx`

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`

`int1/xlogxdx=...............`

(A)log(log x)+ c

(B) 1/2 (logx )²+c

(C) 2log x + c

(D) log x + c

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

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`

Evaluate: `int sqrt(tanx)/(sinxcosx) dx`

Evaluate: `∫8/((x+2)(x^2+4))dx` 

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)`