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Improper Integrals

  • #1

Homework Statement


[itex]\int[/itex] (x-2)-3/2dx

Homework Equations


[itex]\int[/itex]f(x)dx from 0 to ∞ = lim (t[itex]\rightarrow[/itex]∞) [itex]\int[/itex]f(x)dx from 0 to t


The Attempt at a Solution


I have the solution from the solution manual, but I'm just not sure on one of the steps, after you substitute u=(x-2) and du=dx, then integrate u-3/2, but they say that the result to this step is lim(t[itex]\rightarrow[/itex]∞) -2(x-2)-1/2, that is when they integrate u-3/2 they are getting a -2 coefficient, shouldn't it be a -2/3
 

Answers and Replies

  • #2
392
17
Try taking the derivative of the answer to see why it is a -2.

##\int x^n dx = \frac{1}{n+1} x^{n+1}, n \neq -1##
 
  • #3
I'm ummm, I'm face palming right now, thanks.
 
  • #4
392
17
It's okay. Everybody has done something similar at one point or another!
 

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