Area formula In Section 12.3 it was shown that the area of a region enclosed by the polar curve r = g(0) and the rays 0 = a and 0 = B, where B – a s 27, is A = }S² de. Prove this result using the area formula with double integrals.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 6E: Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a...
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Area formula In Section 12.3 it was shown that the area of a
region enclosed by the polar curve r = g(0) and the rays 0 = a
and 0 = B, where B – a s 27, is A = }S² de. Prove this
result using the area formula with double integrals.
Transcribed Image Text:Area formula In Section 12.3 it was shown that the area of a region enclosed by the polar curve r = g(0) and the rays 0 = a and 0 = B, where B – a s 27, is A = }S² de. Prove this result using the area formula with double integrals.
Expert Solution
Step 1

The given result is:

The area of a region enclosed by the polar curve r=gθ and the rays θ=α and θ=β, where β-α2π is,
A=12αβr2dθ.

We have to prove the given result.

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