Question

Find the average value of the function f on the given interval.

f(x) = 7 sin 2x, [−π, π]

Answer 1

is this one of those questions where you solve it via: (f(x_sub_2) - f(x_sub_1))/(x_sub_2 - x_sub_1)
? That is probably what I would try first.

Answer 2

it involves integration ... using \[\int\limits_{-\pi}^{\pi}\]

Answer 3

so then you would include (1/(b-a)) times the integral of that function?

Answer 4

yup

Answer 5

How would u integrate 7sin2x?

Answer 6

i am also just learning integration, but the first thing I do is pull out the multiplicative constant (in our case it looks like that 7)

Answer 7

then we just have to integrate sin(2x). I think that is -(cos2x)/2

Answer 8

sin 2x = 2cosxsinx

Answer 9

I don't think that is the correct result.

Answer 10

that's the identity that's supposed to be used

Answer 11

well, i just confirmed that the indefinite integral of sin(2x) is what I wrote earlier, but if you MUST use 2cosxsinx, then in that case I would do a u-sub (u=sinx, du=cosx dx)

Answer 12

keep in mind that if you decide to go the u-sub route, make sure to change the limits of integration as well.

Answer 13

If i do \[\int\limits_{-\pi}^{\pi}\sin2x\] then should I get it equal to \[-\frac{ 1 }{ 2 }\cos2x\]

Answer 14

without applyinh \[\pi,-\pi\]

Answer 15

right, that seems like the easier way to go to me. That way we don't have to mess with the limits of integration. We can just take 7 times whatever 1/(b-a) amounted to, times your function pi to -pi.

Answer 16

thanks :)

Answer 17

you're welcome.