Consider the given function and the given interval. f$x$ = 2 sin$x$ - sin$2 x$ text(, ) [0 text(, ) pi] (a) Find the avera

Question

3 years ago

14

Consider the given function and the given interval. f$x$ = 2 sin$x$ - sin$2 x$ text(, ) [0 text(, ) pi] (a) Find the avera

ge value fave of f on the given interval. fave = Correct: Your answer is correct. (b) Find c such that fave = f(c). (Enter solutions from smallest to largest. If there are any unused answer boxes, enter NONE in the last boxes. Round the answers to three decimal places.)

Mathematics

1 answer:

Finger [1] · Answer 1 · 2022-06-17T22:37:32+03:00

Finger [1]3 years ago

4 0

a. The average value of $f$ on the given interval is

$\displaystyle f_{\rm ave}=\frac1{\pi-0}\int_0^\pi(2\sin x-\sin2x)\,\mathrm dx=\boxed{\frac4\pi}$

b. Solve for $c$ :

$\dfrac4\pi=2\sin c-\sin2c\implies\boxed{c\approx1.238\text{ or }c\approx2.808}$

Consider the given function and the given interval. f\(x\) = 2 sin\(x\) - sin\(2 x\) text(, ) [0 text(, ) pi] (a) Find the avera