Question

Is there anyway to integrate y=sinx and y=sin(2x)
0 to pi by hand

Answer 1

I have done the problem using my graphing calculator and double check in wolfram.
my solution is 2.50
I broke it up into 2 parts
\[\int\limits_{0}^{1.0471976}\sin(2x)-\sin(x) dx =.25\]
\[\int\limits_{1.0471976}^{\pi}\sin(x)-\sin(2x) dx =2.25\]
total is 2.5

Answer 2

Is there anyway to do it by hand? My professor does not allow calculators but we are using a textbook that requires them.

Answer 3

you know the standard values of sin(pi/2) and sin(pi)

Answer 4

http://www.wolframalpha.com/input/?i=integrate+from+0+to+pi+sin%28x%29

Answer 5

yes, sin(pi) =0 sin(pi/2)=1

Answer 6

where did you break?? you should have broken down at pi/2

Answer 7

I did not, I just stated the above trig values

Answer 8

integrate from 0 to pi/2 sin(x) dx and
integrate form pi/2 to pi sin(x) dx

Answer 9

But my point of intersection is x=1.0471976

Answer 10

pi/2 is not 1.0471976

Answer 11

I got the same result ... I think wolfram is doing something/
http://www.wolframalpha.com/input/?i=integrate+from+0+to+1.0471976+sin%28x%29+%2B+integrate+from+1.0471976+to+pi+sin%28x%29

Answer 12

you forgot sin(2x)

Answer 13

and that value you mentioned is nearly pi/3
http://www.wolframalpha.com/input/?i=pi%2F1.0471976

Answer 14

oops .. sorry.

Answer 15

yes you are correct, it is pi/3

Answer 16

How do I solve it by hand?

Answer 17

sin(x)=sin(2x)

Answer 18

pi/3 has standard values ...and all it's multiples. I guess express it as surds.

Answer 19

what exactly are you trying to do??

Answer 20

wolf can't show steps

Answer 21

I have to do this problem without using any technology

Answer 22

yes ... but is it just integration??

Answer 23

yes

Answer 24

\[\int\limits_{0}^{\frac{\pi}{3}}\sin(2x)-\sin(x) dx + \int\limits_{\frac{\pi}{3}}^{\pi}\sin(x)-\sin(2x) dx\]

Answer 25

why are you breaking it in parts??