Question

int_(from -pi/2 to pi/2) cos t sin^4 t dt
Please, help

Answer 1

Do you know how to do u-substitution?

Answer 2

yeap

Answer 3

let u = sin t ---> du = cos t dt. and then change the limits

Answer 4

try letting u = sin(t)

Answer 5

ok, so the new int will be int_ ( from -1 to 1) u^4 du

Answer 6

is it right?

Answer 7

so far so good yes :)

Answer 8

= [u^5/5] from -1 to 1

Answer 9

Yep, which evaluates to... n_n

Answer 10

so the final answer should be 2/5?

Answer 11

Yep

Answer 12

hold on, look at this http://www.slader.com/textbook/9780538497817-stewart-calculus-7th-edition/1096/exercises/3/ and please, tell me how he can do that. he confused me

Answer 13

I take all numbers out, it quite easy, just pick the int to calculate and be confused with that stuff, how can he let cost sin^4 t = sin^5 t without using u substitute and change the limits

Answer 14

What chapter is that?
I can't really make any sense of the site but I have the book

Answer 15

16.2 cal 3.

Answer 16

problem 3

Answer 17

I can't really make any sense of the stuff at the bottom, but this should help:
http://www.math.ucla.edu/~ronmiech/Calculus_Problems/32B/chap14/section2/906d3/906_3.html