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anonymous
 5 years ago
How do I show that the area of a circle is pi r^2 with integration?
anonymous
 5 years ago
How do I show that the area of a circle is pi r^2 with integration?

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you intefrate the circumference :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02pi r from 0 to radius of circle

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0integrate \[\sqrt{r ^{2}x ^{2}}\] from 0 to r . Multiply by 4

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0what that amounts to is adding up all the circumferences from 0 to the radius whih = area of the circle

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int_{0}^{r}2\pi.r dr\] \[2\pi \int_{0}^{r}r.dr\] \[2\pi \frac{r^2}{2}2\pi \frac{0}{2}=\pi r^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you soo much!!!!

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0youre welcome :) i accidently discovered that when I tried finding the volume of a solid the wrong way lol

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0Hi, Amistre I think what you want to say is \[\int_0^{2\pi}r\,dr\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0watchmath I integrated your formula, but I got 2 pi^2

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0Ah sorry, it should be double integral \(\int_0^{2\pi}\int_0^r r\,drd\theta\) But I guess you haven't learn double integral

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0I think the more traditional one is the following \[2\int_{r}^r\sqrt{r^2x^2}\,dx \] But to compute this integral you need to use the trigonometric substitution.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0r is a constant right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i typed it as i see it :) \[2\pi \int_{0}^{r}r.dr\] its the shell method for area instead of volume

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0area is the sum of all the circumferences of circles from 0 radius to full radius

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0top r might be better expreesed as x tho

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0I see that know amistre :D

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{2\pi r^2}{2}_{0}^{x}\]
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