   Chapter 16, Problem 2P

Chapter
Section
Textbook Problem

Find the positively oriented simple closed curve C for which the value of the line integral∫C (y3 – y) dx – 2x3dy is a maximum.

To determine

To find: The positively oriented simple closed curve C for which the value of the line integral C(y3y)dx2x3dy is a maximum.

Explanation

Given data:

The positively oriented simple closed curve C for which the value of the line integral C(y3y)dx2x3dy .

Formula used:

Write the expression to evaluate the line integral for a function f(x,y) along the curve C .

CP(x,y)dx+Q(x,y)dy=CP(x,y)dx+CQ(x,y)dy (1)

Write the expression for Green’s Theorem.

D(QxPy)dA=CPdx+Qdy (2)

Write the required differential and integration formulae to evaluate the given integral.

ddxxn=nxn1[f(x)]ndx=[f(x)]n+1n+1

Consider the expression C(y3y)dx2x3dy

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