Question

Find the area of the region. Use a graphing utility to verify your result.
y = 6 sin(x) + sin(6x)

the graph goes from x=0 to x=pi

Answer 1

can someone please helpme

Answer 2

satelite can u help me i knwo i ahve to find the integral first but then what

Answer 3

...

Answer 4

\[\int_0^{\pi} 6\sin(x)+\sin(6x)dx\]

Answer 5

you want a graphing utility? here:
http://www.wolframalpha.com/input/?i=integra+0+to+pi+%286sin%28x%29%2Bsin%286x%29%29+dx

Answer 6

Help me satellite73

Answer 7

answer seems to be 12 but the integral is easy enough. antiderivative of
\[6\sin(x)\] is
\[-6\cos(x)\] and antiderivative of
\[\sin(6x)\] is
\[-\frac{1}{6}\cos(6x)\]
so
\[\int 6\sin(x)+\sin(6x) dx=-6\cos(x)-\frac{1}{6}\cos(6x)\]

Answer 8

plug in
\[\pi\] get
\[-6\cos(\pi)-\frac{1}{6}\cos(6\pi)=6-\frac{1}{6}\]plug in 0 get

\[-6\cos(0)-\frac{1}{6}\cos(0)=-6+\frac{1}{6}\] subtract the second from the first and get 12