Evaluate the integral from 1 to sqrt of e: (-4x)/(x^2) dx?

Question

Evaluate the integral from 1 to sqrt of e: (-4x)/(x^2) dx. Please show work. Thanks a bunch.

Answer 1

∫( -4x/(x^2) dx )

First off, we can cancel an x on the top and bottom.

∫(-4/x dx)

Factor the (-4) out of the integral,

(-4) ∫ (1/x dx)

Which we can now integrate easily.

(-4)ln|x| + C

Answer 2

integral (-4x/x^2) dx=integral (-4/x) dx = -4 ln x

evaluate between 1 and e^0.5 means:

-4 (ln e^0.5 - ln 1) = -2

PS: do your own homework

Answer 3

this site should help:

http://www.expertmathtutoring.com/Integral-Differential-Calculator.php