I'm having trouble understanding some of the notation for definite integrals. Is this right?
$$ \int_1^2 (\frac{1}{x^2} - \frac{4}{x^3}) \, dx$$
$$ \int_1^2 x^{-2} - 4x^{-3} \, dx$$
$$ = \int_1^2 x^{-2} \, dx- \int_1^2 4x^{-3} \, dx$$
$$ \left[ -x^{-1} \right ]_1^2 - \left[\frac{4x^{-2}}{-2} \right]_1^2$$
Is this notation right? Or should it be:
$$\left[ -x^{-1} -\frac{4x^{-2}}{-2} \right]_1^2 $$
It's fine. Lord Shark is correct that the second line is better written
$$\int_1^2 \left(x^{-2} - 4x^{-3}\right) \, dx$$
since the length form $dx$ multiplies the entire function $x^{-2} - 4x^{-3}$ and not just the right term, but the potential for confusion in this case is nil.