Posted by **Tracy** on Monday, November 21, 2011 at 9:36pm.

Find the area in the first quadrant bounded by the arc of the circle described by the polar equation

r = (2 sin theta)+(4 cos theta)

A. 5pi/2

B. (5pi/2)+4

C. 5pi

D. 5pi + 8

- Calculus -
**Steve**, Tuesday, November 22, 2011 at 10:23am
Recall that in polar coordinates,

A = Int(1/2 r^2 dθ)

r^2 = 4 sin^2θ + 8sinθcosθ + 16cos^2θ

= 4 + 4sin2θ + 12cos^2θ

= 10 + 4sin2θ + 6cos2θ

A = Int(5 + 2sin2θ + 3cos2θ)dθ [0,pi/2]

= 5t - cos2θ + 3/2 sin2θ [0,pi/2]

= [5pi/2 + 1 + 0] - [0 - 1 + 0]

= 5pi/2 + 2

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