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

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 ______.

Let I₁ = `int_"e"^("e"^2)  1/logx  "d"x` and I₂ = `int_1^2 ("e"^x)/x  "d"x` then 

`int_0^(pi/2) log(tanx)  "d"x` =

Evaluate: `int_(pi/6)^(pi/3) cosx  "d"x`

Evaluate: `int_0^1 "e"^x/sqrt("e"^x - 1)  "d"x`

Evaluate: `int_1^3 (cos(logx))/x  "d"x`

Evaluate: `int_0^1 (1/(1 + x^2)) sin^-1 ((2x)/(1 + x^2))  "d"x`

Evaluate: `int_0^pi 1/(3 + 2sinx + cosx)  "d"x`

Evaluate: `int_0^(π/4) sec^4 x  dx`

If `int_2^e [1/logx - 1/(logx)^2].dx = a + b/log2`, then ______.

Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4

Find the area of the region bounded by the following curves, X-axis and the given lines : x = 0, x = 5, y = 0, y = 4

Find the area of the region bounded by the parabola y² = 16x and its latus rectum.

Solve the following :

Find the area of the region lying between the parabolas y² = 4x and x² = 4y.

Solve the following:

Find the area of the region bounded by the curve y = 4x², Y-axis and the lines y = 1, y = 4.

The area bounded by the parabola y² = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units