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Mathematics 15 Online
OpenStudy (anonymous):

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

OpenStudy (mathteacher1729):

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?

OpenStudy (anonymous):

I don't know how to.

OpenStudy (anonymous):

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

OpenStudy (mathteacher1729):

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

OpenStudy (anonymous):

1/x^2 = x^-2

OpenStudy (mathteacher1729):

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.

OpenStudy (anonymous):

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

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