- #1
tuoni
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Just started learning integration, and although I can manage simple stuff, I've run into problems with some experiments of mine.
http://enes.fi/temp/circle.png
The function for a circle is:
y = \sqrt{r^{2} - x^{2}}
; and Wolfram gives the integral as:
\frac{1}{2}\left[x \cdot \sqrt{r^{2} - x^{2}} + r^{2} \cdot tan^{-1} \left(\frac{x}{\sqrt{r^{2} - x^{2}}}\right)\right]
This in turn results in:
f(b) - f(a) = f(s) - 0
However, it's all wrong!
A radius of 10 means the area is approximately 78.540. Plugging in 10 into the equation results in division by zero. Even trying to integrate from 0 to 1, I get an area of 291.934, when it should be slightly less than 10!
Grrr! What am I doing wrong?
http://enes.fi/temp/circle.png
The function for a circle is:
y = \sqrt{r^{2} - x^{2}}
; and Wolfram gives the integral as:
\frac{1}{2}\left[x \cdot \sqrt{r^{2} - x^{2}} + r^{2} \cdot tan^{-1} \left(\frac{x}{\sqrt{r^{2} - x^{2}}}\right)\right]
This in turn results in:
f(b) - f(a) = f(s) - 0
However, it's all wrong!
A radius of 10 means the area is approximately 78.540. Plugging in 10 into the equation results in division by zero. Even trying to integrate from 0 to 1, I get an area of 291.934, when it should be slightly less than 10!
Grrr! What am I doing wrong?
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