# Evaluate the definite integral. Calculous

• Nov 26th 2012, 09:12 PM
danielhigareda
Evaluate the definite integral. Calculous
need help. I know i got the wrong answer, because i checked in the back of the book, but i have no idea where i messed up. help please

sinx/((1+cosx)^2)dx from the intervals 0 to pie/3
• Nov 26th 2012, 09:18 PM
MarkFL
Re: Evaluate the definite integral. Calculous
It's hard to know where you messed up without seeing your work, but I would try the substitution:

$\displaystyle u=1+\cos(x)\,\therefore\,du=-\sin(x)\,dx$ and the integral becomes:

$\displaystyle -\int_{u(0)}^{u\left(\frac{\pi}{3} \right)}u^{-2}\,du=\int_{\frac{3}{2}}^2 u^{-2}\,du$

Can you proceed from here?
• Nov 26th 2012, 09:26 PM
danielhigareda
Re: Evaluate the definite integral. Calculous
yes thank you very much!!! I messed up on the anti derivative of cosx. I forgot to add the negative. Thank you.
• Nov 26th 2012, 09:27 PM
illicitkush
Re: Evaluate the definite integral. Calculous
Isn't cos(pi/3) = 1/2? Where did you get the 3/2?
• Nov 26th 2012, 09:32 PM
danielhigareda
Re: Evaluate the definite integral. Calculous
you have to add the 1. u= 1 +cosx.
• Nov 26th 2012, 09:33 PM
illicitkush
Re: Evaluate the definite integral. Calculous
the 3/2? not the 2..
• Nov 26th 2012, 09:38 PM
danielhigareda
Re: Evaluate the definite integral. Calculous
ok so to get the 2 you need to plug the 0 to the equation 1+cosx and that gives you 2. to get the 3/2 you plug in pi/3 to the same formula and that gives you 3/2. the reason that the 2 and the 3/2 switch is because there is a negative in the front and that is a rule.
• Nov 26th 2012, 09:40 PM
illicitkush
Re: Evaluate the definite integral. Calculous
Sorry forgot about the 1 lol
• Nov 26th 2012, 09:42 PM
illicitkush
Re: Evaluate the definite integral. Calculous
• Nov 26th 2012, 09:43 PM
danielhigareda
Re: Evaluate the definite integral. Calculous
i got 1/6
• Nov 26th 2012, 09:48 PM
illicitkush
Re: Evaluate the definite integral. Calculous
You dont have to change the U values and flip the b, a. You could just evaluate the integrand and plug in your original values.
• Nov 26th 2012, 09:57 PM
MarkFL
Re: Evaluate the definite integral. Calculous
Yes, I just like for the limits of integration to be in ascending order.
• Nov 26th 2012, 09:58 PM
illicitkush
Re: Evaluate the definite integral. Calculous
Yeah I see how it works out. And also I figured out how it works out on the other problem
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