Question

Calculate the Definite Integral

Answer 1

\[\int\limits_{0}^{2}\frac{ 1 }{ u }- \frac{ 1 }{ u^5 } \]

Answer 2

@surjithayer can you help me out with this one?

Answer 3

do you know how to find an antiderivative?

Answer 4

Yes

Answer 5

what is the antiderivative for this problem?

Answer 6

1/u = ln(x) + C
1/u^5 = -1/4x^4 + C

Answer 7

\[[\ln(2) - \frac{ 1 }{ 4x^4 }] - [\ln(0) - \frac{ 1 }{ 4(0)^4 }\]

Answer 8

thats ment to be 4(2)^4 on the first part

Answer 9

you need to write it as a limit since this is an improper integral

Answer 10

\[\Large\int\limits_{0}^{2}\left(\frac{ 1 }{ u }- \frac{ 1 }{ u^5 }\right)du\]

\[\Large\lim_{t\to0^{+}}\int\limits_{t}^{2}\left(\frac{ 1 }{ u }- \frac{ 1 }{ u^5 }\right)du\]

Answer 11

@zarkon Sorry I had to leave, so I just do the same thing but, put t in instead of 0 ?

Answer 12

your integrand is not defined at 0 so you need to take the limit.