Question

`int_0^(π/8) tan^2 (2x)` is equal to ______.

विकल्प

• `(4 - π)/8`

• `(4 + π)/8`

• `(4 - π)/4`

• `(4 - π)/2`

Answer 1

`int_0^(π/8) tan^2 (2x)` is equal to `underlinebb((4 - π)/8)`.

Explanation:

`int_0^(π/8) tan^2 (2x) dx = int_0^(π/8) [sec^2(2x) - 1] dx`

= `int_0^(π/8) sec^2 (2x) dx - int_0^(π/8) 1 dx`

= `[(tan 2x)/2]_0^(π/8) - [x]_0^(π/8)`

= `1/2 [tan 2(π/8) - tan 2(0)] - [(π/8) - (0)]`

= `1/2 [tan(π/4) - tan(0)] - [π/8]`

= `1/2 [1 - 0] - π/8`

= `1/2 - π/8`

= `(4 - π)/8`