Definite integral

  • Thread starter nameVoid
  • Start date
  • #1
241
0
latex2png.2.php?z=100&eq=%5Cint_%7B1%7D%5E%7B6%7D%20(%5Csqrt%7Bx-2%7D%20)dx.jpg

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,306
48
Welcome to PF nameVoid.
Let's start by finding an anti-derivative (primitive)... you need something which will give you
[tex]\sqrt{x - 2} = (x - 2)^{1/2}[/tex]
when you differentiate it... can you make a wild guess?
 
  • #3
241
0
using the definition
op%7B%5Clim%7D%5Climits_%7Bn%5Cto%20%5Cinfty%7D%5Csum_%7Bi%3D1%7D%5E%7Bn%7Df(x_i%20)%5CDelta%20x.jpg



5Cto%20%5Cinfty%7D%20%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20%5Csqrt%7B(1%2B5i%2Fn)-2%7D%20%20)(5%2Fn)%20.jpg


im not clear on how to expand the expression to distribute the sum
 
  • #4
35,235
7,054
Look at CompuChip's post again. He's not asking you to use the definition of the definite integral, but rather asking you if you can think of a function whose derivative is sqrt(x - 2).

IOW, d/dx(____) = (x - 2)^(1/2).
Can you fill in the blank?
 
  • #5
623
0
Why don't you just do a subst. u = x - 2?
 

Related Threads on Definite integral

Replies
5
Views
734
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
22
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
6
Views
519
  • Last Post
Replies
24
Views
5K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
2K
Top