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

1. anonymous

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

2. cherrilyn

thanks! I'll try it now

3. cherrilyn

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

4. 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.

5. anonymous

good luck :) np

6. anonymous

cos^2 = u^2 :)

7. anonymous

^_^ substitute cos x with u

8. cherrilyn

so u = cos x not cos t?

9. anonymous

lol cost :)

10. 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 ? :)

11. anonymous

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

12. anonymous

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

13. cherrilyn

yes! thank you so much :)

14. anonymous

np ^_^