∫(sinx)^3(cosx)^3dx different answers depending on U-sub?

  • #1

Homework Statement



I expanded (sinx)^3 into ∫[(sinx)^2(sinx)(cosx)^3]dx then to ∫[(1-cosx^2)(sinx)(cosx)^3]dx

so then u = sinx

However the official solution for this problem expands (cosx)^3 to get ∫[(cosx)^2(cos)(sinx)^3]dx then to ∫[(1-sinx^2)(cosx)(sinx)^3]dx

so then u = cosx

So the final answer is almost the same for each method except for the fact that the first answer is in terms of sinx and the second final answer is in terms of cosx (and contains an extra negative sign due to derivative of cosx producing a negative).

So the question is, are these two answers equal even though they consist of completely different functions in the final answer?
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,365
1,032

Homework Statement



I expanded (sinx)^3 into ∫[(sinx)^2(sinx)(cosx)^3]dx then to ∫[(1-cosx^2)(sinx)(cosx)^3]dx

so then u = sinx

However the official solution for this problem expands (cosx)^3 to get ∫[(cosx)^2(cos)(sinx)^3]dx then to ∫[(1-sinx^2)(cosx)(sinx)^3]dx

so then u = cosx

So the final answer is almost the same for each method except for the fact that the first answer is in terms of sinx and the second final answer is in terms of cosx (and contains an extra negative sign due to derivative of cosx producing a negative).

So the question is, are these two answers equal even though they consist of completely different functions in the final answer?
Subtract one answer from the other.

They only differ by a constant.
 
  • #3
Ah interesting, thanks.
 

Related Threads on ∫(sinx)^3(cosx)^3dx different answers depending on U-sub?

Replies
8
Views
585
Replies
4
Views
3K
  • Last Post
Replies
4
Views
12K
  • Last Post
Replies
6
Views
61K
  • Last Post
Replies
7
Views
6K
  • Last Post
Replies
5
Views
14K
Replies
34
Views
5K
  • Last Post
Replies
8
Views
6K
Replies
2
Views
2K
  • Last Post
Replies
5
Views
1K
Top