# Thread: 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
answer is 0.9921556
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
answer is 0.9921556
Where is my error?
Thanks
I don't see an error here.

3. ok, then the other explanation is the answer is inaccurate?