# Math Help - Function approximation

1. ## 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.
$\int^{0.2}_{0.1} \sqrt[3]{1-x^2} dx$
series expansion:
$(1-x^2)^{\frac{1}{3}}=1-\frac{1}{3}x^2-\frac{1}{9}x^4$
so i have:
$\int^{0.2}_{0.1}(1-\frac{1}{3}x^2-\frac{1}{9}x^4) dx$
$=[x-\frac{1}{9}x^3-\frac{1}{45}x^5]^{0.2}_{0.1}$
=0.09921533
Where is my error?
Thanks

2. 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.
$\int^{0.2}_{0.1} \sqrt[3]{1-x^2} dx$
series expansion:
$(1-x^2)^{\frac{1}{3}}=1-\frac{1}{3}x^2-\frac{1}{9}x^4$
so i have:
$\int^{0.2}_{0.1}(1-\frac{1}{3}x^2-\frac{1}{9}x^4) dx$
$=[x-\frac{1}{9}x^3-\frac{1}{45}x^5]^{0.2}_{0.1}$
=0.09921533