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2 0 0 1 2 area 0 1 1 2 2 sin2 d 2 2 1 1

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Unformatted text preview: 2 2 + y− 3 2 2 = 9 2 7. Determine the area between the polar curves r (θ) = 1 + θ and r (θ) = 2 sin (θ) in the first quadrant. 2 0 0 1 π /2 Area= 0 1 1 + θ + θ2 − 2 sin2 (θ) dθ 2 2 1 1 + θ + θ2 − 1 + cos (2θ) dθ = 2 2 0 π /2 π π2 π3 θ 12 13 1 =− + = − + θ + θ + sin (2θ) + 22 6 2 4 8 48 0 π /2 8. Determine the unit tangent vector to r (θ) = 2 sin θ at θ = π and add it to the 6 picture above. Note: x(θ) = r cos θ and y (θ) = r sin θ. dx = 2 cos (2θ). x(θ) = 2 sin θ cos θ = sin (2θ) and dθ d...
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