Can anyone explain me how to do this?

$$\int\limits_{0,5}^{1}\frac{ dx }{ x ^{2} }$$

Question

Can anyone explain me how to do this?

$$\int\limits_{0,5}^{1}\frac{ dx }{ x ^{2} }$$

experimentx · Answer

how do you do this$$ \int  \frac{1}{x^2} dx$$

kamille · Answer

I know I need to insert numbers when I have done the integral, but I haven't learn at school how to integral when x is in denominator

kamille · Answer

thats why I am asking for help (for a rule?)

anonymous · Answer

Rewrite the integral as an exponential with x to a negative power, instead of as a fraction. Then use the basic power rule for integration.

kamille · Answer

well, once I have done it and my teacher told that I can't write like that, because it should be written with ln, Are you talking about this?

$$\int\limits_{0,5}^{1}=x^{-2}dx$$

experimentx · Answer

when the power is -1 ... i.e $ \displaystyle \frac{1}{x} = x^{-1}$ that's a different case.
when the power is not -1, use the usual power rule.

kamille · Answer

so I can write is as I have written above? : ) Thanks a lot, it always confuses me!

anonymous · Answer

Yes, what you've written is fine (just don't put the equal sign within the integral). The case with 1/x has an integral that gives you ln(x), but that is usually the only exception to the rule with fractions and x with negative exponents.

kamille · Answer

oh, okay! Thank you a lot, guys!