• Support PF! Buy your school textbooks, materials and every day products Here!

Integration (by parts) check my work

  • Thread starter Aerosion
  • Start date
  • #1
53
0

Homework Statement



[tex]\int x^2*cosx dx[/tex]

Homework Equations





The Attempt at a Solution



Okay, so I started by making...
u=x^2
du=2x
dv=cos(x)
v=-sin(x)

Then I made the rudimentary equation:

[tex]\int x^2 * cos(x) dx = -x^2*sin(x) + \int 2x * sin(x) dx[/tex]

Then I took the last integration problem (the one all the way on the right) and did integration by parts on that one again, to make:

u=2x
du=2
dv=sin(x)
v=-cos(x)

to make...

[tex]\int x^2 * cos(x) dx = -x^2 * sin(x) + 2x * sin(x) + \int 2 * cos(x) dx[/tex]

I evaluated the last integration problem to be -2*sin(x), and got a final answer of sin(x)(-x^2+2x-2) (after factoring). Of course, my calculator says this is wrong, so where'd I mess up?

Thanks. (I'm getting better with Latex, btw)
 
Last edited:

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
8,107
73
In your first step, if dv=cos(x)dx, then v=sin(x) (no minus sign).
 

Related Threads on Integration (by parts) check my work

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
1
Views
941
Replies
17
Views
2K
Replies
2
Views
2K
Replies
9
Views
1K
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
2
Views
959
  • Last Post
Replies
2
Views
787
  • Last Post
Replies
4
Views
1K
Top