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
Answer This Question
Related Questions
 Calculus  Find the area under one arch of a cycloid describe by the parametric ...
 precalculus  Is this right? Convert the polar coordinate (14, 5pi/3) to ...
 Calculus  Find the area of the region which is bounded by the polar curves ...
 Calculus  Find the area of the region which is bounded by the polar curves ...
 Calculus  Find the area of the region which is bounded by the polar curves ...
 Calculus  Find the area of the region which is bounded by the polar curves ...
 Math  Solve (sinx1)(cosx 1/2) = 0 where 0≤x<2pi a) pi/3, pi/2, 5pi/3...
 trig  using the fact that 5pi/8=1/2(5pi/8) and the half angle identity for cos ...
 Maths  Find the area of the region which is bounded by the polar curves theta =...
 Math  Find the area of the region which is bounded by the polar curves theta =...
More Related Questions