# Function approximation

• Feb 16th 2010, 09:12 PM
arze
Function approximation
Use the first three terms of the series expansion as an approximation for the function to be integrated. Estimate the value of the definite integral.
$\displaystyle \int^{0.2}_{0.1} \sqrt[3]{1-x^2} dx$
series expansion:
$\displaystyle (1-x^2)^{\frac{1}{3}}=1-\frac{1}{3}x^2-\frac{1}{9}x^4$
so i have:
$\displaystyle \int^{0.2}_{0.1}(1-\frac{1}{3}x^2-\frac{1}{9}x^4) dx$
$\displaystyle =[x-\frac{1}{9}x^3-\frac{1}{45}x^5]^{0.2}_{0.1}$
=0.09921533
Where is my error?
Thanks
• Feb 17th 2010, 06:10 AM
Jester
Quote:

Originally Posted by arze
Use the first three terms of the series expansion as an approximation for the function to be integrated. Estimate the value of the definite integral.
$\displaystyle \int^{0.2}_{0.1} \sqrt[3]{1-x^2} dx$
series expansion:
$\displaystyle (1-x^2)^{\frac{1}{3}}=1-\frac{1}{3}x^2-\frac{1}{9}x^4$
so i have:
$\displaystyle \int^{0.2}_{0.1}(1-\frac{1}{3}x^2-\frac{1}{9}x^4) dx$
$\displaystyle =[x-\frac{1}{9}x^3-\frac{1}{45}x^5]^{0.2}_{0.1}$
=0.09921533