   Chapter 10.3, Problem 80E

Chapter
Section
Textbook Problem

Area In Exercises 79 and 80, find the area of the region. (Use the result of Exercise 77.) x = 2 cot θ y = 2 sin 2 θ 0 < θ < π To determine

To Calculate:

The area of the region on the interval 0θπ.

Explanation

Given:

Ellipse of parametric equations:

x=2cotθ

y=2sin2θ and 0θπ

Given graph is:

Formula Used:

If y is a continuous function of x on the interval axb, where x=f(t) and y=g(t), then area of the curve in the interval axb is given by,

abydx=t1t2g(t)f'(t)dt

where f(t1)=a, f(t2)=b and both g and f' are continuous on [t1,t2]

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