Use a double integral to find the area of the region. [Solved]

The top answer is very close, but incorrect.
The right answer is 25/6*(3sqrt(3) 2pi.

(x 5)^2 y^2 = 25 – (1)
x^2 y^2 = 25 – (2)

Find the intersection:
(1) (2)
10x 25 = 0 > x = 5/2 > y = 5rt(3)/2
change to polar: (r, /3)

Thus, the area
= 4 * (25 / 6 253 / 8)
= 50 / 3 253 / 2

rdrd, (5/2)sec r 5, 0 /3
[(1/2)r, (5/2)sec r 5] d, 0 /3
= [25/2 (1/2)(25/4)sec] d, 0 /3
= (25/2) (25/8)tan, 0 /3
= (25/2)/3 (25/8)3
= 25 / 6 253 / 8

Thus, the area
= 4 * (25 / 6 253 / 8)
= 50 / 3 253 / 2

The top answer is very close, but incorrect.
The right answer is 25/6*(3sqrt(3) 2pi.

This post is last updated on hrtanswers.com at Date : 1st of September – 2022

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