[SOLVED] Integral estimation

**topsquark** · March 30th 2008, 03:51 PM

I just had a student ask me the question:

Using 20 terms, estimate f(0.6) where
$f(x) = \int_0^x \frac{dt}{1 + t^3}$

The student was trying to do this using a geometric series to represent the integrand. I haven't yet looked it up in my Calc book, but if I ever knew the method I've completely forgotten it. Any takers?

Thanks!
-Dan

**Krizalid** · March 30th 2008, 03:55 PM

$f(x) = \int_0^x {\left\{ {\sum\limits_{k\, = \,0}^\infty {( - 1)^k t^{3k} } } \right\}\,dt} .$

After interchanging sum & integral you'll get its series representation.

**topsquark** · March 30th 2008, 04:24 PM

Originally Posted by Krizalid

$f(x) = \int_0^x {\left\{ {\sum\limits_{k\, = \,0}^\infty {( - 1)^k t^{3k} } } \right\}\,dt} .$

After interchanging sum & integral you'll get its series representation.

Ahhhhh! I had my head stuck in Maclaurin series. Okay, thanks!

-Dan

**ThePerfectHacker** · March 30th 2008, 05:19 PM

How about proving the accurarcy after using 20 terms? That sounds like a more interesting problem.

**topsquark** · March 30th 2008, 06:08 PM

Originally Posted by ThePerfectHacker

How about proving the accurarcy after using 20 terms? That sounds like a more interesting problem.

(snorts) These are Calc I High School students. Maybe AP maybe not. I'm not going to go into that kind of thing with them unless they force me to with hot irons, kicking and screaming "You can't have your pudding if you don't eat your meat!"

-Dan

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