Let D be the region bounded by the parabola y = x2 and the curve y = sin x, and let P represent a path going around D counterclockwise. Compute ∫P F ·dr where F(x,y) = ∇f and f(x,y) = x2ye4x−y^2

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let D be the region bounded by the parabola y = x2 and the curve
y = sin x, and let P represent a path going around D counterclockwise.
Compute ∫P F ·dr where F(x,y) = ∇f and f(x,y) = x2ye4x−y^2
.

Expert Solution
Step 1

If the input of the function is more than one, such functions are called multivariable functions. The integral in the form PFx,y·dr involves the integral over a specified path. In this problem, we have to evaluate the integral  PFx,y·dr, over the path formed by intersecting y=sinx and y=x2, where F(x,y)=f and f=x2ye4x-y2. The function y=sinx is a periodic function and y=x2 represents a parabola, that opens up. 

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