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2. Let C be the line segment from (0,5,0) to (2,0,-1). Calculate S (x²+z?)dx + (x2...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the curve from above. point in the anti-clockwise direction when viewed Calculate the line integral (e (e sin y+ 4) dy+(e(cos z+ sin z)+ay) dz. cos x2yz) dx + (b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the...
3. Suppose that C is the oriented curve consisting of the line segment from origin to (2,0), the vertical line segment from (2,0) to (2,8), and the arc of the cubic from y=x from (2,8) back to the origin. Evaluate (2x + y) dx + (x2 + 2y) dy. Hint: What color is a lime?
5. Compute the line integral ſc fds, where a) C is the line segment from (3,4,0) to (1,4, 2) and f(x, y, z) = x + y2. b) C is the curve y = x2 from (0,0) to (3,9) and f(x,y) = 3x. c) C is the upper half of the circle of radius 2 from (2,0) to (-2,0) and f(x,y) = y.
Evaluate the line integral. fr de x² dx + y²dy, where C is the arc of the circle x2 + y2 = 4 from (2,0) to (0,2) followed by the line segment from (0, 2) to (4,3).
Use Green’s Theorem to compute ∮c (2xy−y+ 1) dx+ (x2−ln(1 +y)) dy where C is the top half of the circle x2+y2= 4 along with the line segment connecting (−2,0) and (2,0)
Let W be the solid: 0 < x,0 <y, 0 <z < 20 – 2y - X., What is S? S 20-2y 20-2y-2 SJSW 1DV = ſ s 1 dz dar dy S 0 0 Question 18 W is the same solid as in Question 17. What is T?: 20 T 20-2y-2 SSSw 1dV = SS S 1 dz dy dx. 0 0 0 A) 10 B) 20 C) 10 – C 2 D) 10 - y
Let W be the solid: 0 < 3,0 <y, 0 <z< 20 – 2y – X., What is S?: S 20-2y 20-2y- S SSSw 1DV = S 1 dz do dy 0 0 0 Question 18 W is the same solid as in Question 17. What is T?: 20 T 20-2y-2 SSSw 1 DV = SS S 1 dz dy dx. 0 0 0 A) 10 B) 20 - 3 C C) 10 – D) 10 - y
Write an iterated integral for SSS fex,y,z) av. S = {(x, y, z): 0 sxs8,0 sy s5,0<zs (5 - 6x - 2y)} 5 S 5-6x - 2y f(x, y, z) dz dy dx 5 8 5 f(x, y, z) dz dy dx s 8 5 5 - 6x - 2y f(x, y, z) dz dy dx 5 666 8 5 5 - 6x - 2y f(x, y, z) dx dy dz
must be in the order of dx dy dz 2. ONLY Find the limits when DV is written as dx dy dz (the integration has to be done in this order). SSS, f (x,y,z)dV where f(x, y, z) = 1 – x and D is the solid that lies in the first octant and below the plane 3x + 2y + z = 6.
Let E be the solid bounded by y+z=1 z=0 and y=x^2 a) Bind z, and provide (but do not evaluate) the triple integral with the plane described horizontally simple (dz dx dy) b) Bind z, and provide (but do not evaluate) the triple integral with the plane described vertically simple (dz dy dx) c) Bind x, and provide (but do not evaluate) the triple integral with the plane described horizontally simple (dx dy dz) d) Bind x, and provide (but...