This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: dz dy dx . (b) Evaluate the integral. 4. Calculate the circulation of the eld F = 3 xy i + sin 16 ( y ) j clockwise around the boundary of the triangle with vertices (0 , 0), (1 , 1), and (2 , 0). 5. Consider the surface S dened by x 2 + y 2 = 4, 0 z 3, and oriented with normal vectors n pointing away from the z-axis. Compute the ux of the vector eld F = 2 xz i + yz 2 j + p x + y 2 k across S in the direction of n . 6. Consider a paraboloid hut with base z = 0 and roof z = 2-x 2-y 2 . We assume that a < 2, so that the hut is not inside the cylinder x 2 + y 2 = a 2 . Let R be the region that is inside the hut and inside the cylinder x 2 + y 2 = a 2 . (a) Compute the volume of R . (b) Set b = a 2 . Find b if the volume of R is equal to 3 4 (the volume of the hut). 1...
View Full Document