# Mean value theorem for integrals.

1. Oct 13, 2006

### bobbarkernar

find c such that (f)average=f(c)

f(x)=7sin(x)-sin(2x), [0,pi]

ok so i found (f)average= 14/pi

then i tried to compute:
7sin(c)-sin(2c)= (14/pi)

but the answers i got were wrong.

2. Oct 13, 2006

$$7\sin c - \sin 2c = \frac{14}{\pi}$$
$$7\sin c - 2\sin c \cos c = \frac{14}{\pi}$$.
Let $$a = \sin c$$ and $$b = \cos c$$.
Then $$7a-2ab = \frac{14}{\pi}$$. We also know that $$a^{2} + b^{2} = 1$$. Can you go from there?