Posted by **Bobby** on Wednesday, March 10, 2010 at 9:33am.

How do you prove that the total area of a four-petaled rose r=sin2x is equal to one-half the area of the circumscribed circle?

- calculus -
**drwls**, Wednesday, March 10, 2010 at 10:29am
Use a polar coordinate integration to get the area inside the rose. The circumscribed circle area is, of course, pi, since rmax = 1

For the rose, the area is

S (1/2)r^2 dx

(for x integrated from 0 to 2 pi

= S (1/2)sin^2x dx

"S" denotes an integral sign.

=(1/2)[(x/2) -(1/4)(sin2x)]@x=2pi -

(1/2)[(x/2) -(1/4)(sin2x)]@x=0

= (1/2)*pi

qed

## Answer This Question

## Related Questions

- Ms. Sue Please help!!! - Ahhh... thank you "A square and an equilateral triangle...
- 8th grade math - circle A has a raduis that is twice the length og the raduis of...
- area of circle - The radius of a circle is 8ft. I have 60ft of tile. Is this ...
- calculus - Find the smallest possible area of an isosceles triangle that is ...
- math - A circle has an area of 25 pi cm^2.If a circle is drawn within that ...
- calculus(Lab) - Well, first graph the graph of f(x)=-1/10x^2 + 3 2. We are going...
- solid mensuration - A circle has an area equal to 25 pi sq.cm. Its diameter AB ...
- Calculus - How do you prove area of a circle? Integrate an incremental area ...
- geometry - Theres a circle with an equilateral triangle in the middle. The ...
- Maths - If the volume of a cylindrical block is equal to 800cm^3 prove that the ...

More Related Questions