
Evaluate the integral using the fundamental linear theory s y dx + xdy + Ź dz,...
Which of the following is equivalent to -y-dx + xdy + xz-dz where C is the intersection of y + z = 3 and x' + y = 4, oriented counterclockwise when viewed from above. Hint: Consider the surface S lying inside of the slanted circle. Turn it into an integral over S using Stokes' theorem. 2012 (-psine +8rsin? - 8r) drde s "S*(-7°sino +er+sin? "O 21 2 1 (-r?sin?@ +6rsin 8 - 3) drdo 1, " \ *c+2rsin?aydrde 211...
Problem 1: A) Evaluate the iterated integral. A1) S S**** S*yz dy dz dx Ans: A2) SS, (x + 2y) dV, where E is bounded by the parabolic cylinder y - xand the planes x -2, x = y, and z o Ans: And
(1 point) Evaluate the integral. 16 16- S. 1 (a2y2z2)1/2 dy dz dx 16-r 0
(1 point) Evaluate the integral. 16 16- S. 1 (a2y2z2)1/2 dy dz dx 16-r 0
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)
Do not evaluate, rewrite the integral using spherical coordinates 25-x² - y2 1 dz dx dy 05 NUS y=0 X-O Z=o
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
Problem 18. 7/2 (1 point) Evaluate the iterated integral AIT cos(x+y+z) dz dx dy. Answer:
Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 2 6 dx S √1-x² 0 V3 2 6 dx 5 0 V1 - (Type an exact answer.)
25 2 6 Evaluate the integral S SS 3 cos (x2) -dx dy dz by changing the order of integration in an appropriate way. 417 o o Зу
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr-
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...