0

$$\int_{\pi/4}^{\pi/2} \cot^5 \phi \csc^3 \phi \;d\phi$$

My final answer is: $$\frac{8}{105} - \sqrt 2 \left(\frac{22}{105}\right)$$

This is apparently the wrong answer. Did I make a mistake somewhere ...

  • I made the substitution let $u = \csc$
    • New upper limit of integration: $1$
    • New lower limit of integration: $\sqrt2$
Guest
  • 323
  • 1
    Without showing more of your work, it's sort of difficult to tell you at what point you went wrong. Did you use $ \ du \ = \ -\cot \phi \ \csc \phi \ d\phi \ $ ? That will swap the integration limits after substitution. (A brief visit with WA suggests that might be what is at issue...) – colormegone May 18 '14 at 03:44
  • @RecklessReckoner I see my mistake now, it was with du, I put u = cscϕ but put du = cotϕ cscϕ dϕ – Guest May 18 '14 at 03:48
  • 1
    Otherwise, your answer looked fine (sign errors get us one and all!). Keep in mind that everything you do in integration with the "partners" secant and tangent work the same for cosecant and cotangent, except for a sign "flip". – colormegone May 18 '14 at 03:51
  • @Guest Could you please add a brief answer explaining how you resolved the issue so this question doesn't sit in the "Unanswered" queue for another five years when you've already figured out what went wrong? It's perfectly possible, even encouraged, in some cases, to answer your own question. – Robert Howard Mar 12 '19 at 02:41

0 Answers0