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Flux on a tetrahedron Find the upward flux of the field F = 〈x, y, z〉 across the plane
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Calculus: Early Transcendentals (3rd Edition)
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- Work integrals Given the force field F, find the work required to move an object on the given oriented curve. F = ⟨y, -x⟩ on the line segment from (1, 2) to (0, 0) followedby the line segment from (0, 0) to (0, 4)arrow_forwardFlux across curves in a vector field Consider the vector fieldF = ⟨y, x⟩ shown in the figure.a. Compute the outward flux across the quarter-circleC: r(t) = ⟨2 cos t, 2 sin t⟩ , for 0 ≤ t ≤ π/2.b. Compute the outward flux across the quarter-circleC: r(t) = ⟨2 cos t, 2 sin t⟩ , for π/2 ≤ t ≤ π.c. Explain why the flux across the quarter-circle in the third quadrant equals the flux computed in part (a). d. Explain why the flux across the quarter-circle in the fourth quadrant equals the flux computed in part (b).e. What is the outward flux across the full circle?arrow_forwardLine integrals of vector fields in the plane Given the followingvector fields and oriented curves C, evaluate ∫C F ⋅ T ds. F = ⟨-y, x⟩ on the semicircle r(t) = ⟨4 cos t, 4 sin t⟩ , for 0 ≤ t ≤ πarrow_forward
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