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Use the Divergence Theorem to evaluate the flux F(x, y, z) = Consider the shown work. div(F) S F. ds. (x³,0, 2³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 d = • (x²) + (0) + (2²³) = 3 (x² + 2²) dx дz 1 [[F. ds = ₁³ (x² + 2²) dv = [' ' ' 3 (x² + 2²) dx dydz D 3 dV W

Use the Divergence Theorem to evaluate the flux F(x, y, z) = Consider the shown work. div(F) S F. ds. (x³,0, 2³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 d = • (x²) + (0) + (2²³) = 3 (x² + 2²) dx дz 1 [[F. ds = ₁³ (x² + 2²) dv = [' ' ' 3 (x² + 2²) dx dydz D 3 dV W

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Use the Divergence Theorem to evaluate the flux Consider the shown work. F(x, y, z) = (x³, 0, z³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 Us div(F) = The shown work is ə Ə (x²¹) + (0) + (2²) = 3 (x² + 2²) dx дz 1 [[¸ F · ds = [], ³ (x² + 2²) av = [ "' "' [² 3 (x² + 2²) dx dy dz F. 3 W Complete the statement regarding if the shown work is correct. (Express IS₁ S not correct because only the bounds needs to be changed ✓ only the bounds needs to be changed div(F) needs to be corrected no changes should be made only the integrand needs to be changed spherical coordinates should be used mumours in cautt form. The Symon F. ds. ( the bounds are not correct, but the integrand is correct S F. ds. y given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 notation and fractions where needed.) Therefore,
Transcribed Image Text:Use the Divergence Theorem to evaluate the flux Consider the shown work. F(x, y, z) = (x³, 0, z³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 Us div(F) = The shown work is ə Ə (x²¹) + (0) + (2²) = 3 (x² + 2²) dx дz 1 [[¸ F · ds = [], ³ (x² + 2²) av = [ "' "' [² 3 (x² + 2²) dx dy dz F. 3 W Complete the statement regarding if the shown work is correct. (Express IS₁ S not correct because only the bounds needs to be changed ✓ only the bounds needs to be changed div(F) needs to be corrected no changes should be made only the integrand needs to be changed spherical coordinates should be used mumours in cautt form. The Symon F. ds. ( the bounds are not correct, but the integrand is correct S F. ds. y given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 notation and fractions where needed.) Therefore,
Use the Divergence Theorem to evaluate the flux F(x, y, z) = (x³, 0, z³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 (Express numbers in exact form. Use symbolic notation and fractions where needed.) Is F. ds. F. ds =
Transcribed Image Text:Use the Divergence Theorem to evaluate the flux F(x, y, z) = (x³, 0, z³), S is the boundary given by x² + y² + z² ≤ 64, x ≥ 0, y ≥ 0, z ≥ 0 (Express numbers in exact form. Use symbolic notation and fractions where needed.) Is F. ds. F. ds =
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