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Chapter 6: Q9P (page 314)

Evaluate each of the following integrals in the easiest way you can.

鈭�(2ydx-3xdy)around the square bounded by x=3,x=5,y=1andy=3.

Short Answer

Expert verified

The solution to this problem is I=-20.

Step by step solution

01

Given Information.

The given information is鈭�(2ydx-3xdy)

02

Definition of Green’s Theorem.

The Green's theorem connects a line integral around a simple closed curve C to a double integral over the plane region D circumscribed by C in vector calculus. Stokes' theorem has a two-dimensional special case.

03

Find the solution.

Write the values of P and Q.

P=2yQ=-3x

Find the difference of their differentiation

鈭�Q鈭�x-鈭�P鈭�y=-3-2=-5

The integral is in the form mentioned below.

l=-5鈭�13鈭�35dxdy=-5脳4=-20

Hence, the solution to this problem is l-20

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