## A community for students. Sign up today

Here's the question you clicked on:

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

• This Question is Closed
1. amistre64

you intefrate the circumference :)

2. amistre64

integrate even lol

3. amistre64

2pi r from 0 to radius of circle

4. anonymous

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

5. amistre64

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

6. amistre64

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

7. anonymous

Thank you soo much!!!!

8. amistre64

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

9. watchmath

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

10. anonymous

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

11. 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

12. anonymous

not yet

13. 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.

14. anonymous

r is a constant right?

15. amistre64

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

16. amistre64

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

17. amistre64

top r might be better expreesed as x tho

18. watchmath

I see that know amistre :D

19. amistre64

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

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy