# Calculus

posted by .

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x^2+y^2=64 and x^2 - 8x + y^2 = 0.

• Calculus -

14 pi

• Calculus -

the answer u gave me is incorrect. and please tell me the method u tried

• Calculus -

You don't need Calculus to do this.
The outer circle has centre at (0,0) and has radius 8
The other circle has centre (4,0) and radius 4, so the touch at (8,0)
The big circle has area 64π, so the area in the first quad is 16π
The smaller circle has area 16π and half of it lies in quad I, so the area in there is 8π

So the area between the big circle and the little circle in quad I = 16π-8π = 8π

## Similar Questions

1. ### Calculus

A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of …
2. ### Calculus

A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of …
3. ### Math

A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of …
4. ### Maths

A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of …
5. ### calculus

Use a double integral to find the area of the smaller region bounded by the spiral rtheta=1, the circles r=1 and r=3, and the polar axis. I just need help with setting up the integral.
6. ### Calculus AP

Let R be the region in the first quadrant bounded by the graph y=3-√x the horizontal line y=1, and the y-axis as shown in the figure to the right. Please show all work. 1. Find the area of R 2. Write but do not evaluate, an integral …
7. ### Calculus (polar coordinates)

Use polar coordinates to set up the double integral x dA, where the bounds are given by the region lying in the intersection of the 2 circles r = 2 sin (theta) and r = 2 cos theta. Thanks for any help!
8. ### AP Calculus AB

Which integral gives the area of the region in the first quadrant bounded by the axes, y = e^x, x = e^y, and the line x = 4?
9. ### Calc

Use spherical coordinates. Evaluate Triple integral SSSE where E lies between the spheres x^2 + y^2 + z^2 = 25 and x^2 + y^2 + z^2 = 49 in the first octant.