Question

Find the average value fave of the function f on the given interval. f(t) = e^sin(t) cos(t), [0, π/2]

Answer 1

The question is related to integration and we have to used the following formula

$\frac{1}{b-a}\int\limits^a_b {f(x)} \, dx$

$\frac{1}{\pi /2 -0}\int\limits^0_{\pi/2} {e^{sin t}cos t } \, dt$

$= \frac{2}{\pi}(e^{sin t})_{0}^{ \pi /2}$

$=\frac{2}{\pi}(e^{sin(\pi/2)} -e^{sin0})$

$=\frac{2}{\pi}(e -1)$