Question

`int_0^pi sin^2x.cos^2x  dx` = ______ 

Options

• 0

• 1

• 2

• 3

Answer 1

`int_0^pi sin^2x.cos^2x  dx` = 0

Explanation:

Let I = `int_0^pi sin^2x.cos^3x  dx`

= `int_0^pi sin^2(pi - x) . cos^3(pi - x)dx` .........`[∵ int_0^a f(x)dx = int_0^a f(a - x)dx]`

= `int_0^pi sin^2x(-cosx)^3dx`

= `-int_0^pi sin^2x . cos^3x dx`

∴ I = -I

∴ 2I = 0

∴ I = 0