cherrilyn
  • cherrilyn
with reduction formula and techniques, evaluate the integral of cos^2(sint)costdt
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
let u = cost and du = sint ^_^ that's all, give it a try now
cherrilyn
  • cherrilyn
thanks! I'll try it now
cherrilyn
  • cherrilyn
If u = cost and du=sint...what should I do with the cos^2?

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anonymous
  • anonymous
u = sint, du =cost dt. Then from here it becomes cos^2(u) du. Which turns into cos(u)*cos(u) which you can integrate with integration by parts.
anonymous
  • anonymous
good luck :) np
anonymous
  • anonymous
cos^2 = u^2 :)
anonymous
  • anonymous
^_^ substitute cos x with u
cherrilyn
  • cherrilyn
so u = cos x not cos t?
anonymous
  • anonymous
lol cost :)
anonymous
  • anonymous
here : \[\int\limits \cos^2 t (cost) (sint) dt =-\int\limits u^3 du \rightarrow = - \frac{u^4}{4} + c \] \[= \frac{\cos^4 t}{4} + c\] better ? :)
anonymous
  • anonymous
I forgot the minus in the last step, add it ^_^
anonymous
  • anonymous
remember u = cos t, so du= - sin t
cherrilyn
  • cherrilyn
yes! thank you so much :)
anonymous
  • anonymous
np ^_^

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