Question

find area of shaded region. (I have attempted this problem multiple times and keep getting an incorrect answer, help :/ )

Answer 1

Holy cha ca MOly LOL @whpalmer4 @sourwing @jim_thompson5910

Answer 2

wait is it 8π + 3√3

Answer 3

It would help others help you if you were to find some way of sharing images of your work with those who might be able to help you. currently I have no idea regarding what you've been able to do and what you've thought of doing.

I'd suggest that you find the points of intersection of these two circles. One of the is obviously (0,0). what about the other one? How would you determine the angle and the radius of that point (to express the point in polar coordinates?

Draw a straight line through the 2 points of intersection. Determine the angle (theta) that this line makes with the positive x-axis. Use the area formula for polar coordinates to find (separately) (a) the area enclosed by your straight line and the smaller circle, and (b) the area enclosed by your line and the larger circle. Add these two areas together, and you've got the total area.

type out the general formula for area in polar coordinates here, please, to use it as a starting point.

Answer 4

well this would be the formula for area..

Answer 5

*scratches head im going to go to my professor on this one

Answer 6

and the other point at which they intersect is at pi/6

Answer 7

I have not actually sought the coordinates of the intersection of the two curves, but must say that your "pi/6" looks quite reasonable. and your area formula is correct.

Decide which of the 2 given equations describes the smaller circle. As required by the area formula you've typed in, square this equation and divide the result by 2. Integrate this last result from theta=pi/6 to theta=pi/2. that will be the area defined by the smaller square and the straight line!

Do the same thing to find the area defined by the line and the larger circle. Good luck!!