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

Evaluate the following using properties of definite integral:

`int_(-1)^1 log ((2 - x)/(2 + x))  "d"x`

Evaluate the following using properties of definite integral:

`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x)  "d"x`

Evaluate the following using properties of definite integral:

`int_0^1 log (1/x - 1)  "d"x`

Evaluate the following using properties of definite integral:

`int_0^1 x/((1 - x)^(3/4))  "d"x`

Evaluate the following:

Γ(4)

Evaluate the following:

`Γ (9/2)`

Evaluate the following:

`int_0^oo "e"^(-mx) x^6 "d"x`

Evaluate the following:

`int_0^oo "e"^(-4x) x^4  "d"x`

Evaluate the following:

`int_0^oo "e"^(- x/2) x^5  "d"x`

If f(x) = `{{:(x^2"e"^(-2x)",", x ≥ 0),(0",", "otherwise"):}`, then evaluate `int_0^oo "f"(x) "d"x`

Evaluate the following integrals as the limit of the sum:

`int_0^1 (x + 4)  "d"x`

Evaluate the following integrals as the limit of the sum:

`int_1^3 x  "d"x`

Evaluate the following integrals as the limit of the sum:

`int_1^3 (2x + 3)  "d"x`

Evaluate the following integrals as the limit of the sum:

`int_0^1 x^2  "d"x`

Choose the correct alternative:

`int_0^1 (2x + 1)  "d"x` is

Choose the correct alternative:

`int_0^oo "e"^(-2x)  "d"x` is

Choose the correct alternative:

`int_(-1)^1 x^3 "e"^(x^4)  "d"x` is

Choose the correct alternative:

If f(x) is a continuous function and a < c < b, then `int_"a"^"c" f(x)  "d"x + int_"c"^"b" f(x)  "d"x` is

Choose the correct alternative:

The value of `int_(- pi/2)^(pi/2) cos  x  "d"x` is

Choose the correct alternative:

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function Γ(n) when n = 8 is