Answered: Evaluate the integral of the function…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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Evaluate the integral of the function f (x, y) = 4 along the circle of radius 2 oriented clock-wise whose parametrization is given by
r(t) = (2 cos 0, 2 sin 0), 0 E [0, 27]
(2 decimals is ok)
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Expert Solution

Step 1

Given that $f (x, y) = 4$ along the circle of radius 2 oriented clock wise whose parametrization is given by $r (t) = <2 \cos θ, 2 \sin θ>, θ \in [0, 2 π]$ .

The objective is to find the integral for the function.

So $\iint_{C} f (x, y) d S$

Now the integral can be rewritten as,

$I = \int_{0}^{2 π} f (r (θ)) . r' (θ) d θ$

It is given that

$f (x, y) = 4 f (r (t)) = 4$

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