Mastering the Definite Integral: A Comprehensive Guide

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nameVoid
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latex2png.2.php?z=100&eq=%5Cint_%7B1%7D%5E%7B6%7D%20(%5Csqrt%7Bx-2%7D%20)dx.jpg

 
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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?
 
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
 
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?
 
Why don't you just do a subst. u = x - 2?