Ask your own question, for FREE!
Mathematics 27 Online
OpenStudy (anonymous):

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

OpenStudy (amistre64):

you intefrate the circumference :)

OpenStudy (amistre64):

integrate even lol

OpenStudy (amistre64):

2pi r from 0 to radius of circle

OpenStudy (anonymous):

integrate \[\sqrt{r ^{2}-x ^{2}}\] from 0 to r . Multiply by 4

OpenStudy (amistre64):

what that amounts to is adding up all the circumferences from 0 to the radius whih = area of the circle

OpenStudy (amistre64):

\[\int_{0}^{r}2\pi.r dr\] \[2\pi \int_{0}^{r}r.dr\] \[2\pi \frac{r^2}{2}-2\pi \frac{0}{2}=\pi r^2\]

OpenStudy (anonymous):

Thank you soo much!!!!

OpenStudy (amistre64):

youre welcome :) i accidently discovered that when I tried finding the volume of a solid the wrong way lol

OpenStudy (watchmath):

Hi, Amistre I think what you want to say is \[\int_0^{2\pi}r\,dr\]

OpenStudy (anonymous):

watchmath I integrated your formula, but I got 2 pi^2

OpenStudy (watchmath):

Ah 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

OpenStudy (anonymous):

not yet

OpenStudy (watchmath):

I think the more traditional one is the following \[2\int_{-r}^r\sqrt{r^2-x^2}\,dx \] But to compute this integral you need to use the trigonometric substitution.

OpenStudy (anonymous):

r is a constant right?

OpenStudy (amistre64):

i typed it as i see it :) \[2\pi \int_{0}^{r}r.dr\] its the shell method for area instead of volume

OpenStudy (amistre64):

area is the sum of all the circumferences of circles from 0 radius to full radius

OpenStudy (amistre64):

top r might be better expreesed as x tho

OpenStudy (watchmath):

I see that know amistre :D

OpenStudy (amistre64):

\[\frac{2\pi r^2}{2}|_{0}^{x}\]

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!