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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

you intefrate the circumference :)
integrate even lol
2pi r from 0 to radius of circle

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

integrate \[\sqrt{r ^{2}-x ^{2}}\] from 0 to r . Multiply by 4
what that amounts to is adding up all the circumferences from 0 to the radius whih = area of the circle
\[\int_{0}^{r}2\pi.r dr\] \[2\pi \int_{0}^{r}r.dr\] \[2\pi \frac{r^2}{2}-2\pi \frac{0}{2}=\pi r^2\]
Thank you soo much!!!!
youre welcome :) i accidently discovered that when I tried finding the volume of a solid the wrong way lol
Hi, Amistre I think what you want to say is \[\int_0^{2\pi}r\,dr\]
watchmath I integrated your formula, but I got 2 pi^2
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
not yet
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.
r is a constant right?
i typed it as i see it :) \[2\pi \int_{0}^{r}r.dr\] its the shell method for area instead of volume
area is the sum of all the circumferences of circles from 0 radius to full radius
top r might be better expreesed as x tho
I see that know amistre :D
\[\frac{2\pi r^2}{2}|_{0}^{x}\]

Not the answer you are looking for?

Search for more explanations.

Ask your own question