Can someone please see if I did it right or not?

Substitute with

Do I have to add +C?

Thanks a lot

Printable View

- Jan 17th 2011, 04:59 PMPPSSAGWA Complicated Integral

Can someone please see if I did it right or not?

Substitute with

Do I have to add +C?

Thanks a lot - Jan 17th 2011, 05:03 PMdwsmith
- Jan 17th 2011, 05:04 PMPPSSAGW
Yeah I later changed it.

- Jan 17th 2011, 05:04 PMdwsmith
- Jan 17th 2011, 05:05 PMPPSSAGW
Thanks. I'm new to LaTex.

- Jan 17th 2011, 05:07 PMPPSSAGW
- Jan 17th 2011, 05:10 PMdwsmith
- Jan 18th 2011, 07:11 AMHallsofIvy
There is no need to actually do the integral- this is an exercise in using the "Fundamental Theorem of Calculus":

Here, because the upper limit is rather than x, you need to use the substitution . That way the upper limit is (assuming x is positive). Now and so that and the integral becomes

and, by the Fundamental Theorem of Mathematics, the derivative of that is

just by replacing u in the integrand by x. - Jan 18th 2011, 10:58 AMdwsmith
- Jan 18th 2011, 12:45 PMHallsofIvy
Good point but since, unless the intent was

It really is very close to a trivial question! - Jan 18th 2011, 12:46 PMdwsmith