Question

The value of `int_0^pitan^2(theta/3) d theta` is ______.

Options

• `pi+sqrt3`

• `3sqrt3-pi`

• `sqrt3-pi`

• `pi-sqrt3`

Answer 1

The value of `int_0^pitan^2(theta/3) d theta` is `underlinebb(3sqrt3-pi)`.

Explanation:

`int_0^pitan^2(theta/3)d theta = int_0^pi[sec^2(theta/3)-1].d theta`

= `int_0^pi sec^2(theta/3)d theta-int_0^pi d theta`

= `[(tan  theta/3)/(1/3)]_0^pi - [theta]_0^pi`

= `(3 tan  pi/3 - 3tan  0/3)-(pi-0)`

= `(3xxsqrt3 - pi)`