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

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

`(1)/(\pi /2 -0)\int\limits^0_(\pi/2) {e^(sin t)cos t } \, dt`

`= (2)/(\pi)(e^(sin t))_(0)^( \pi /2)`

`=(2)/(\pi)(e^(sin(\pi/2)) -e^(sin0))`

`=(2)/(\pi)(e -1)`