Thread: Evaluate the definite integral. Calculous

1. 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

2. 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:

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

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

Can you proceed from here?

3. 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.

4. Re: Evaluate the definite integral. Calculous

Isn't cos(pi/3) = 1/2? Where did you get the 3/2?

5. Re: Evaluate the definite integral. Calculous

you have to add the 1. u= 1 +cosx.

6. Re: Evaluate the definite integral. Calculous

the 3/2? not the 2..

7. 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.

8. Re: Evaluate the definite integral. Calculous

Sorry forgot about the 1 lol

i got 1/6

11. 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.

12. Re: Evaluate the definite integral. Calculous

Yes, I just like for the limits of integration to be in ascending order.

13. 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