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
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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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 involves the integral over a specified path. In this problem, we have to evaluate the integral , over the path formed by intersecting and , where and . The function is a periodic function and represents a parabola, that opens up.
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