Question

If `I_n = int_0^(pi/4) tan^n theta  "d"theta " then " I_8 + I_6` equals ______.

Options

• `1/4`

• `1/5`

• `1/6`

• `1/7`

Answer 1

If `I_n = int_0^(pi/4) tan^n theta  "d"theta " then " I_8 + I_6` equals `1/7`.

Explanation:

`I_8 + I_6 = int_0^(pi/4) (tan^8theta + tan^6theta) "d"theta`

= `int_0^(pi/4) tan^6theta sec^2theta "d"theta`

Put tan θ = t ⇒ sec²θ dθ = dt

`therefore I_8 + I_6 = int_0^1 "t"^6 "dt" = ["t"^7/7]_0^1 = 1/7`