What am I doing wrong in this integral?

Question

legomyego180 · Answer

$$\int\limits_{\frac{ \pi }{ 3 }}^{\frac{ \pi }{ 2 }}\frac{ (3\sin(x)) }{ (4+2\cos(x))^2 }$$

legomyego180 · Answer

$$u=2\cos(x)+4$$
$$du=-2\sin(x)$$

$$-\frac{ 2 }{ 3 }\int\limits_{\frac{ \pi }{ 3 }}^{\frac{ \pi }{ 2 }}\frac{ 1}{ u^2 }$$

legomyego180 · Answer

that should be negative, sorry

myininaya · Answer

i think i see ...
$$du=-2 \sin(x) dx \ \frac{3}{-2} du= 3 \sin(x) dx$$
you should have -3/2 out in front

legomyego180 · Answer

Oh yea, you're right

legomyego180 · Answer

Im still getting the wrong answer though

myininaya · Answer

did you want to show the rest of  your work

holsteremission · Answer

Check the limits. They don't stay the same once you change the variable.

legomyego180 · Answer

$$-\frac{ 3 }{ 2 }\left[ -\frac{ 1 }{ 4 }+\frac{ 1 }{ 5 } \right]$$

legomyego180 · Answer

Thats what I got after evaluating my bounds

holsteremission · Answer

That's correct.

legomyego180 · Answer

Oh I have to change the bounds by plugging into u?

legomyego180 · Answer

Oh I typed it into wolfram wrong...

>.<

legomyego180 · Answer

Thank you guys, I appreciate the help. I was afraid I had forgotten how to do integrals overnight...

canimcan · Answer

Just write it again and you'll solve it.