HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Important Questions for Mathematics and Statistics

`int sqrt((9 + x)/(9 - x))  "d"x`

`int 1/(2 +  cosx - sinx)  "d"x`

`int sin(logx)  "d"x`

`int "e"^(sin^(-1_x))[(x + sqrt(1 - x^2))/sqrt(1 - x^2)] "d"x`

`int (x^2 + x -1)/(x^2 + x - 6)  "d"x`

`int (x + sinx)/(1 - cosx)  "d"x`

Evaluate:

`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`

`int  ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1])  "d"x`

Evaluate: `int (dx)/(2 + cos x - sin x)`

If u and v ore differentiable functions of x. then prove that:

`int uv  dx = u intv  dx - int [(du)/(d) intv  dx]dx`

Hence evaluate `intlog x  dx`

`int cos^3x  dx` = ______.

Write `int cotx  dx`.

Evaluate: `int (2x^2 - 3)/((x^2 - 5)(x^2 + 4))dx`

Evaluate:

`int1/(x^2 + 25)dx`

Evaluate the following integrals as limit of a sum:

\[\int\limits_0^2 (3x^2 - 1)\cdot dx\]

Evaluate: `int_0^1 (x^2 - 2)/(x^2 + 1).dx`

Evaluate: `int_0^(pi/2) x sin x.dx`

Evaluate: `int_0^π sin^3x (1 + 2cosx)(1 + cosx)^2.dx`

Choose the correct option from the given alternatives : 

`int_0^(pi/2) (sin^2x*dx)/(1 + cosx)^2` = ______.

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