Hi.
I am having some problems getting how to figure out what to do when I need to plug a letter into the integral.
∫ 1/ x^2 from 0 to 1. I integrate and get -1/x and since we can´t use 0 put a instead : (-1/a -1). Why does this equal oo? Do I plug some number in for a? How does this work? Also, which number do I evaluate (stick into the integral) first? Why?
Another example would be ∫ 1/x from 0 to 1. That comes out to ln x . There we have the same problem as before. We use a letter instead of 0. What then? How is it evaluated? I don´t get what to do when I need to plug a letter into the integral? What does it mean when I end up with some a letter and a number when I am evaluating?
Thank you!
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Answers & Comments
Verified answer
If you look at the curve you will see that as x → 0, f(x) → ∞
So the area under the curve between 0 and 1 is infinite.
∫ 1/ x^2 from 0 to 1. I integrate and get -1/x is correct
-1/x ] 0 to 1 = lim a → 0 (-1/1 - -1/a)
= lim a → 0 (-1 + 1/a)
→ 1 + ∞
→ ∞
use limits,
no kidding