approximate integral using power series

**rcmango** · February 5th 2009, 11:26 AM

0 int 0.2

1/(1+x^5) dx

need to use power series to approximate the definate integral.

thankyou for help on this one!

**Danny** · February 5th 2009, 02:43 PM

Originally Posted by rcmango

0 int 0.2

1/(1+x^5) dx

need to use power series to approximate the definate integral.

thankyou for help on this one!

From the geometric power series

$\frac{1}{1+x} = 1 - x + x^2 - x^3 + - \cdots$

$\frac{1}{1+x^5} = 1 - x^5 + x^{10} - x^{15} + - \cdots$

so

$\int_0^{0.2}\frac{1}{1+x^5}\, dx = \int_0^{0.2} 1 - x^5 + x^{10} - x^{15} + - \cdots \, dx$

and integrate term-by-term (you won't need a lot of terms to get a really accurate answer)

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