Ask
your own question, for FREE!

Mathematics
29 Online

OpenStudy (anonymous):

Evaluate the definite integral: cos(x)/sin^9(x) on the interval from [pi/6,pi/2]

Still Need Help?

Join the QuestionCove community and study together with friends!

OpenStudy (anonymous):

\[\text{Let } u = sin(x) \implies du = cos(x)\ dx\] Should be pretty straight forward from there.

OpenStudy (anonymous):

does sin^9(x) become sin^-9(x)?

OpenStudy (anonymous):

If you like, sure. It actually becomes \(u^{-9}\)

OpenStudy (anonymous):

so i will come to get -1/8(sin(x)^-8 and i will plug in pi/2 and pi/6 from there?

OpenStudy (anonymous):

\[\text{Let } u = sin(x) \implies du = cos(x)\ dx\]\[\large\implies \int_{\pi/6}^{\pi/2}\frac{cos(x)}{sin^9(x)}\ dx\]\[\large=\int_{1/2}^1\frac{1}{u^9}\ du\]\[\large = \int_{1/2}^1 u^{-9} \]\[\large= -\left.\frac{1}{8u^8}\right|^1_{1/2}\]

Still Need Help?

Join the QuestionCove community and study together with friends!

OpenStudy (anonymous):

Or yeah, plugging in the original limits is also fine if you convert back to the original function instead of using u.

Can't find your answer?
Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!

Join our real-time social learning platform and learn together with your friends!

Latest Questions

KyledaGreat:
u201c She's Leaving Homeu201d Wednesday morning at five o'clock as The day begins Silently closing her bedroom door Leaving the note that she hoped would sa

8 minutes ago
0 Replies
0 Medals

PureSoulless:
What are some steps that I would need to follow to grow a lettuce without dirt or

22 minutes ago
1 Reply
0 Medals

PureSoulless:
What is the science behind hallucinations (All kinds of hallucination)

4 hours ago
0 Replies
0 Medals

PureSoulless:
What is the science behind not being able to draw from pure imagination. (I know with enough practice, you can draw from pure imagination, but most of us ca

2 hours ago
2 Replies
0 Medals

KyledaGreat:
Happiness I was born with so much love I burst each time the sun risesI reserve t

10 minutes ago
4 Replies
1 Medal

MistyMoonlight22:
Dear QuestionCove Community, I wanted to inform you that I'll be taking a break from participating in discussions here on QuestionCove.

11 hours ago
2 Replies
0 Medals

cJanonymous:
i dont understand the meaning and how to use the terms like debit and credit, amo

1 day ago
2 Replies
0 Medals