Question

integrate 1/x^1.005

Answer 1

first write is as

x ^ n

Answer 2

using 1 / x^m = x^-m

Answer 3

yes, x^-1.005. is this right?

Answer 4

good, so you have to integrate it now,
(with respect to x, i'm assuming)

\[\int x^{-1.005}\,\mathrm dx\]

are you given limits or not?

Answer 5

yes dx and also i am given the limits, but i am wondering on how to integrate that first.

Answer 6

the limits arent necessary at this moment, am i correct? or is it?

Answer 7

the general case is

\[\int x^n\,\mathrm dx = \frac{x^{n+1}}{n+1}+c\]
for the indefinite integral

and
\[\int\limits_{x_i}^{x_f} x^n\,\mathrm dx = \left.\frac{x^{n+1}}{n+1}\right|_{x=x_i}^{x=x_f}\]
for the definite integral

Answer 8

i remember it as: "add one to the index, and divide by the new index"

Answer 9

so the integration is the same before substituting the values of limits right?

Answer 10

yeah, pretty much

Answer 11

yeah, that's what i did, but in the solution i have here, it says its integral is -(200/x^0.005)

Answer 12

im confused by the 200

Answer 13

what did you get?

Answer 14

my answer is x^0.005/0.005

Answer 15

what is 1/0.005 equal to?

Answer 16

oh wait, is it because 0.005 is 1/200?

Answer 17

yes!

Answer 18

i just entered on the calcu. lol

Answer 19

yeah im having second thoughts lol. maybe the solution made the x the denominator again?

Answer 20

but now im confused where the negative came from. the answer is -(200/x^0.005)

Answer 21

x^(-1.005)


x^(-0.005) / -0.005 = -200 x^(-0.005)
= -200 / x^(0.005)

Answer 22

oh yes of course i forgot its -0.005 not 0.005. haha. hey thanks man, appreciate the help

Answer 23

if this is the indefinite integral (no limits)
don't forget to +c

Answer 24

yup thanks again!