Question

http://prntscr.com/9rbx82

Answer 1

Mean Value Theorem? Please, would you look that up and share here what you find? We need to go through that Theorem first, and then apply it to the problem at hand.

Answer 2

I'd also suggest that you draw the situation given you; that would make it clearer what we're trying to find / do.

Answer 3

do you want the equation or the definition?

Answer 4

HI!!

Answer 5

\[\frac{1}{b-a}\int_a^bf(x)dx=f(c)\] fro some \(c\)
is that what you are using?

Answer 6

yes

Answer 7

ok so we start with \[\frac{1}{\pi}\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}4\cos(x)dx=4\cos(c)\]

Answer 8

the 4 is a red herring so you can ignore it, i.e. divide both sides by 4

Answer 9

what do you mean by "red herring"?

Answer 10

i mean ignore it, i.e. divide both sides by 4 before you begin

Answer 11

now that i look more carefully, i have no idea how you are going to solve for \(c\)
the integral is easy enough though

Answer 12

can you compute the integral?

Answer 13

oooh now i see, it wants a decimal as an answer
ok we can do that then

Answer 14

8/pi=4cos(c)

Answer 15

yeah or \[\frac{2}{\pi}=\cos(c)\]

Answer 16

wait, it would just be 8/pi=cos(c)

Answer 17

so since it asks for a decimal, our only job now is a calculator exercise \[c=\cos^{-1}(\frac{2}{\pi})\]

Answer 18

no, you had it right the first time, then divide both sides by 4

Answer 19

which i tried to convince you to do at the start, but whatever ...

Answer 20

now comes the calculator part
http://www.wolframalpha.com/input/?i=arccos%282%2Fpi%29

Answer 21

.881

Answer 22

that is what i get too!

Answer 23

lol i mean that is what wolframalpha gets too

Answer 24

awesome, thank you!
Can you help me with another problem?

Answer 25

\[\color\magenta\heartsuit\]
sure, why not?

Answer 26

but make a new post, too hard to scroll down