So I need help integrating this: sqrt(1+cosx)dx
And integrating :cosxsinxdx on the interval 0 to 2pi.
Witht the second one I can only get to solutions that result in zero because the final always equals the initial.
Ideas?
So I need help integrating this: sqrt(1+cosx)dx
And integrating :cosxsinxdx on the interval 0 to 2pi.
Witht the second one I can only get to solutions that result in zero because the final always equals the initial.
Ideas?
I used half angle identities and it worked with the first one. Is there an explanation as to why half angle identities work better sometimes?
For the second one I'm entirely sure its not zero. It goes from ds=3asinxcosxdx and the answer is 6a so somehow integrating sinxcosxdx should be 2.
Hmmm
Just to add my 2 cents with definite integrals use a little geometery to see if you answer is reasonable.
Notice that $\displaystyle \displaystyle \sin(x)\cos(x)=\frac{1}{2}\sin(2x)$
This is a sine function with a peroid of Pi. Whenever you integrate since or cosine over one complete peroid you will get zero. Graph it.
So if you integrate over two peroids you will still get zero.