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cherrilyn
 5 years ago
with reduction formula and techniques, evaluate the integral of cos^2(sint)costdt
cherrilyn
 5 years ago
with reduction formula and techniques, evaluate the integral of cos^2(sint)costdt

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let u = cost and du = sint ^_^ that's all, give it a try now

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0thanks! I'll try it now

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0If u = cost and du=sint...what should I do with the cos^2?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0u = 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
 5 years ago
Best ResponseYou've already chosen the best response.0^_^ substitute cos x with u

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0so u = cos x not cos t?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here : \[\int\limits \cos^2 t (cost) (sint) dt =\int\limits u^3 du \rightarrow =  \frac{u^4}{4} + c \] \[= \frac{\cos^4 t}{4} + c\] better ? :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I forgot the minus in the last step, add it ^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0remember u = cos t, so du=  sin t

cherrilyn
 5 years ago
Best ResponseYou've already chosen the best response.0yes! thank you so much :)
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