HSC Commerce कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Choose the correct alternative:

`int_2^4 ("d"x)/x` is

Choose the correct alternative:

`int_0^1 sqrt(x^4 (1 - x)^2)  "d"x` is

Choose the correct alternative:

If `int_0^1 f(x)  "d"x = 1, int_0^1 x  f(x)  "d"x = "a"`, and `int_0^1 x^2 f(x)  "d"x = "a"^2`, then `int_0^1 ("a" - x)^2 f(x)  "d"x` is

Choose the correct alternative:

The value of `int_2^3 f(5 - 3)  "d"x - int_2^3 f(x)  "d"x` is

Choose the correct alternative:

`int_0^4 (sqrt(x) + 1/sqrt(x))  "d"x` is

Choose the correct alternative:

`int_0^(pi/3) tan x  "d"x` is

Evaluate the following integral:

`int 1/(sqrt(x + 2) - sqrt(x + 3))  "d"x`

Evaluate the following integral:

`int ("d"x)/(2 - 3x - 2x^2)`

Evaluate the following integral:

`int ("d"x)/("e"^x + 6 + 5"e"^-x)`

Evaluate the following integral:

`int sqrt(2x^2 - 3)  "d"x`

Evaluate the following integral:

`sqrt(9x^2 + 12x + 3)  "d"x`

Evaluate the following integral:

`int (x + 1)^2 log x  "d"x`

Evaluate the following integral:

`int log (x - sqrt(x^2 - 1)) "d"x`

Evaluate the following integral:

`int_0^1 sqrt(x(x - 1))  "d"x`

Evaluate the following integral:

`int_(-1)^1 x^2 "e"^(-2x)  "d"x`

Evaluate the following integral:

`int_0^3 (x dx)/(sqrt(x + 1)+ sqrt(5x + 1))`

Using Integration, find the area of the region bounded the line 2y + x = 8, the x-axis and the lines x = 2, x = 4

Find the area bounded by the lines y – 2x – 4 = 0, y = 0, y = 3 and the y-axis

Calculate the area bounded by the parabola y² = 4ax and its latus rectum

Find the area bounded by the line y = x and x-axis and the ordinates x = 1, x = 2