Question

How do I use the Fundamental Theorem of Calculus to evaluate the definite integral?

Answer 1

That image is too large, do you have a smaller one? :-p

Seriously though, you would break up the integral into

\[\huge \int_1^2 x^{-2}\ dx\] and
\[\huge -\int_1^2 x^{-3}\ dx\]

Can you evaluate each of these integrals separately?

Answer 2

I don't know how to.

Answer 3

use the power rule.... nothing special....

Answer 4

The problem is asking "What function, when you take its derivative... gives you \(\huge x^{-2}\)?

Answer 5

1/x^2 = x^-2

Answer 6

You did correct algebra -- those are two equivalent ways of writing the same function, but the calculus asks for a relationship between the derivatives of functions.

Answer 7

power rule:
\(\large \int x^ndx=\frac{x^{n+1}}{n+1}+C,\space{ }n \ne1 \)