8. cos xsin y dx +(3xy+sin x cos y) dy C:boundary of the region lying between the graphs of y= and y = Vx

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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8.
cos xsin y dx +(3xy+sin x cos y) dy
C:boundary of the region lying between the graphs of y=
and y = Vx
Transcribed Image Text:8. cos xsin y dx +(3xy+sin x cos y) dy C:boundary of the region lying between the graphs of y= and y = Vx
Expert Solution
Step 1 Given

Given:  Ccosxsinydx+(3xy+sinxcosy)dy...................(i)

where C is bounded by y=x4  and  y=x

To find- Integration of the given integral i.e. area of the region C bounded by y=x4  and  y=x

Green's Theorem: Let R be a simply connected region with a piecewise smooth boundary C, oriented counterclockwise (that is, C is traversed once so that the region R always lie to the left ). If P and Q have continuous first partial derivatives in an open region containing R,then

CPdx+Qdy=RPy-QxdA..............................(ii)

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