A) Use Green's theorem to compute the area inside the ellipse Use the fact that the area can be written as Hint: (t) = 17 cos(t). The area is x2 y² + 152 17² 1₂ ¸dz dy = 2/1/2₁-4₁ dx + x dy. Jap || 1.

Q: Find the area inside one petal of the curve r = 4 sin(20).

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Q: A) Use Green's theorem to compute the area inside the = 1. 2² y² ellipse + 19² 14² Use the fact that…

A: (A). Given,                            x2192+y2142=1,      use the fact that the area can be written…

Q: Use the parametric equations of an ellipse x = 4 cos 0 y = 13 sin 0 0≤0 ≤2T to find the area that it…

A: Given x = 4 cos θy = 13 sin θ0 ≤ θ ≤ 2π

Q: Q1. Calculate the area of the region lies inside the diagram (r= 4 cos 20) and outside the circle (r…

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Q: a) Find the area of the reason that lies inside the circle r = 3a cos 0 and outside the cardioid r=…

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Q: Sketch the curve. r=2 sin 8 1 2 -1 OO O O -1 1 -2 -1 O Find the area that it encloses. 1

A: r=2-sinθ

Q: Graph of the function y = cos 2x What is the area of the region bounded by the x = 15°, x = 45°…

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Q: Use the parametric equations of an ellipse, x = 3 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2T, to find the area…

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Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: 2y-3a) and the x-axis 2. Find the area enclosed by r = a cos 30 II YOLUMES OF REVOLUTION

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Q: Draw the curve r = 2 cos 20 and calculate the area enclosed by this curve

A: Given r=2cos2θ

Q: Find the area

A: Step 1: Step 2: Step 3:na Step 4:

Q: Find the area of the region inside the cardiod r = 2+2 cos 0 and inside the cardiod r = 2 2 cos 0 -…

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Q: (D) Sketch the graph r =1- cos 0 and find the area enclosed by r =1- cos 0.

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Q: Q-Find the area of the region that outside r= 2 sin (e) and inside r= (1+cos e)? %3D

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Q: Sketch the curve. r=2 sin 8 1 2 -1 0.0 O C -1 1 -2 -1 Find the area that it encloses. 1

A: Given polar curve is r = 2-sinθ The above is standard curve. put, θ = π2  we get r= 2- sinπ2 = 2 -1…

Q: - Find the area of the ellipse which is parametrically expressed as =a cos o and y=b sin ø, and…

A: To find the area of the ellipse which is parametrically expressed by the below equations.…

Q: Find the area inside the graph of r = 5 - 3 sin (0) and outside the graph of r = 5 - 3 cos(0).

A: We need to find the area inside the graph of  and outside the graph of .We know that the area of a…

Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: c) Find the curve length of the lemniscate of the area Inside the lemniscate r² = 6 cos 20 and…

A: Solution:-