HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Important Questions

`int 1/sqrt(x^2 - a^2)dx` = ______.

Solve: `int sqrt(4x^2 + 5)dx`

`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`

The value of `int ("d"x)/(sqrt(1 - x))` is ______.

Complete the following activity:

`int_0^2 dx/(4 + x - x^2) `

= `int_0^2 dx/(-x^2 + square + square)`

= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`

= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`

= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`

Find the area of the region bounded by the parabola y² = 16x and the line x = 4. 

Find the area of the region bounded by the following curves, the X-axis and the given lines:

y = x² + 1, x = 0, x = 3

Area of the region bounded by y = x⁴, x = 1, x = 5 and the X-axis is _______.

Using definite integration, area of the circle x² + y² = 49 is _______.

Find the area of the region bounded by y = x², the X-axis and x = 1, x = 4.

Find the area of the region bounded by the parabola y² = 25x and the line x = 5.

Choose the correct alternative:

Area of the region bounded by the parabola y² = 25x and the lines x = 5 is ______

The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x)  "d"x`

Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3

Find the area of the region bounded by the curve y = (x² + 2)², the X-axis and the lines x = 1 and x = 3

Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5

The slope of a tangent to the curve y = 3x² – x + 1 at (1, 3) is ______.

The area of the region bounded by the curve y = x², x = 0, x = 3, and the X-axis is ______.

Find the area between the two curves (parabolas)

y² = 7x and x² = 7y.

Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.