E Let C₁ be the curve parameterized by r(t) = (cos² t, sint) where t = [-]. Let C₂ be the line segment from (0, 1) to (0, -1). (a) Points (x, y) on curve C₁ all lie on the graph of an equation x = f(y) for some simple function f. What is that function? (b) Use Green's theorem to find the flux of F = xy² i + (y- ) j out of the region bounded between C₁ and C₂. (c) Use your answer to part (b) to find the left-to-right flux of F = xy² i+(y-ez³)j across C₁ only without having to take the flux integral over C₁ directly.

E Let C₁ be the curve parameterized by r(t) = (cos² t, sint) where t = [-]. Let C₂ be the line segment from (0, 1) to (0, -1). (a) Points (x, y) on curve C₁ all lie on the graph of an equation x = f(y) for some simple function f. What is that function? (b) Use Green's theorem to find the flux of F = xy² i + (y- ) j out of the region bounded between C₁ and C₂. (c) Use your answer to part (b) to find the left-to-right flux of F = xy² i+(y-ez³)j across C₁ only without having to take the flux integral over C₁ directly.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.1: Antiderivatives

Problem 45E

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