Question

`int_0^(2pi) cosec^7xdx` = ______

विकल्प

• 0

• 1

• 4

• 2π

Answer 1

`int_0^(2pi) cosec^7xdx` = 0

Explanation:

We know, `int_0^(2a)f(x)dx` = 0, if f(2a − x) = −f(x)

Let f(x) = cosec²x.

Now, f(2π − x) = cosec⁷(2π − x) = − cosec⁷x = −f(x)

`therefore int_0^(2pi) cosec^7xdx = 0  ...["Using the property" int_0^(2a) f(x)dx = 0,  "if"  f(2a − x) = −f(x)]`