Question

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

Answer 1

let u = cost and du = sint ^_^ that's all, give it a try now

Answer 2

thanks! I'll try it now

Answer 3

If u = cost and du=sint...what should I do with the cos^2?

Answer 4

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.

Answer 5

good luck :) np

Answer 6

cos^2 = u^2 :)

Answer 7

^_^ substitute cos x with u

Answer 8

so u = cos x not cos t?

Answer 9

lol cost :)

Answer 10

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 ? :)

Answer 11

I forgot the minus in the last step, add it ^_^

Answer 12

remember u = cos t, so du= - sin t

Answer 13

yes! thank you so much :)

Answer 14

np ^_^