Question

what is the integral of the function 1/x^7 from 1 to infinity? I already know it converges to a number because of p = 7 is greater than 1

Answer 1

hello!

Answer 2

well.. first find the integral .. which is (-1/6)(1/x^6).. then apply limits..

Answer 3

improper integrals eh ..... havent tried them out yet ..

Answer 4

well, with the integral of the function, it looks like what ever n could be from 1 to infinity, it would be too small to change the value of (-1/6), so maybe the answer is -1/6. I will try it

Answer 5

nope

Answer 6

answer is +(1/6)

Answer 7

you would get.. 0 - (-1/6) = 1/6

Answer 8

oh, whoops, math error! thanks

Answer 9

x^-7 ints up to x^-6/-6

\[\frac{-1}{6(inf)^6}-\frac{-1}{6(1)^6}=0-(-1/6)=1/6\]

Answer 10

okay, now i see it better

Answer 11

Thanks everyone!

Answer 12

These integral should be written

\[\int\limits_{1}^{\infty}\frac{1}{x^7}dx=\lim_{t\to\infty}\int\limits_{1}^{t}\frac{1}{x^7}dx\]

Integrate like you normally would using the FTC then take the limit