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Suppose that C is the positively oriented square with vertices (-3,-1), (1, −1 ), (1, 71), and (-). Let F(x, y) = P(x, y)i + Q(x, y)j where (a) (b) P(x, y) = (cos(x) + x²)y 23 Q(x, y) = 1+x+ 3 (*) Applying the Green's theorem, transform [F to a double integral. (*) Find the value of F.dr F.dr

Suppose that C is the positively oriented square with vertices (-3,-1), (1, −1 ), (1, 71), and (-). Let F(x, y) = P(x, y)i + Q(x, y)j where (a) (b) P(x, y) = (cos(x) + x²)y 23 Q(x, y) = 1+x+ 3 (*) Applying the Green's theorem, transform [F to a double integral. (*) Find the value of F.dr F.dr

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. Suppose that C is the positively oriented square with vertices (-1, 1), (1, 1), (1, 1), and (-). Let F(x, y) = P(x, y)i + Q(x, y)j where (a) (b) P(x, y) = (cos(x) + x²)y x³ 3 to a double integral. Q(x, y) = 1 + x + (*) Applying the Green's theorem, transform [.F. (*) Find the value of F. dr [F F. dr
Transcribed Image Text:7. Suppose that C is the positively oriented square with vertices (-1, 1), (1, 1), (1, 1), and (-). Let F(x, y) = P(x, y)i + Q(x, y)j where (a) (b) P(x, y) = (cos(x) + x²)y x³ 3 to a double integral. Q(x, y) = 1 + x + (*) Applying the Green's theorem, transform [.F. (*) Find the value of F. dr [F F. dr
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If F=Px,yi+Qx,yj is a vector-valued function, then according to Green's theorem ∫CF·dr=∬S∂Q∂x-∂P∂ydxdy, where C is the boundary of the surface. In this problem Px,y=cosx+x2y, Q=1+x+x33 and C is the positively oriented curve with vertices -π2,-π2,π2,-π2,π2,π2,-π2,π2. We have to find the value of ∫CF·dr

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