I think this question is pretty basic, but I would be very happy if you could help
Find the area under the curve y = (x-2)^-2 + 1, from x = -1 to x = 1
Do I integrate y = (x-2)^-2 + 1?? How teacher uses some random hard to understand process where she finds the derivate and uses that to adjust the integral o.O
Thanks!!
Lachlan
If you let u= x-2, differentiating both sides give du= dx (was that what you meant by "finds the derivate"); when x= -1 , u= -1-2= -3, and when x= 1, u= 1-2= -1. Now replace each of those things in your integral by its value in terms of u, becomes . That is NOT some "random hard to understand process". That is a very logical, standard method known as "integration by substitution".