$\displaystyle\int_0^{\pi/4} an^4 x\, dx = ?$

Question

$\displaystyle\int_0^{\pi/4} 	an^4 x\, dx = ?$

Accepted Answer

A. $\dfrac{\pi}{4} - \dfrac{2}{3}$

**Reduction:** $I_n = \int_0^{\pi/4} 	an^n x\, dx$, $I_n + I_{n-2} = 1/(n-1)$. $I_0 = \pi/4$. $I_2 = 1 - \pi/4$.
$I_4 = 1/3 - I_2 = 1/3 - 1 + \pi/4 = \pi/4 - 2/3$.

Answer

$\dfrac{\pi}{4}$

Answer

$\dfrac{1}{3}$

Answer

$\dfrac{1}{3} - \dfrac{\pi}{4} + \dfrac{\pi}{2}$... — actually $\dfrac{3\pi - 8}{12}$ form

$\displaystyle\int_0^{\pi/4} \tan^4 x\, dx = ?$

Keep practising Unit 6B: Definite Integration & Riemann Sums