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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....
Multivariable Calculus
3. Evaluate the line integral |(x+2y)ds where Cis the curve defined by x=t, y , ostsi. (6 points)
question 4
4. Evaluate the iterated integrals x + y2 +z’ds where C is the curve parameterized by i(t)=(t,cos(2t),sin(2t)) on 0 S1s 21,
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
Use Stokes' Theorem to evaluate sta curl F. ds. F(x, y, z) = xyzi + xyj + x2yzk, S consists of the top and four sides (but not the bottom of the cube with vertices (+3, +3, +3), oriented outward. Need Help? Read It Watch It Talk to a Tutor Submit Answer 33. [-/2.5 Points] DETAILS SCALC8 16.8.018. MY NOTES ASK YOUR Evaluate le (y + 5 sin(x)) dx + (z2 + 3 cos(y)) dy + x3 dz where C...
0 2y+3 S4) ss x- 2y X+ y ୧ dxdy 1-y (x-2y)² integralinin değerini bulunuz. (15 puan)
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
Q1: 4pnts Evaluate the following integrals along the given curve C. (a) (32) ds. C : The section of the parabola y = x2 from the origin to the point (3,9) (b) yds,C:2 4 with y 20 0S152 (c) / C:x=cos t, y = sin t, z = t, ysin z ds, 0 t〈2π C : x e-t cos t, y = e-t sin t, z = e-t,
Q1: 4pnts Evaluate the following integrals along the given curve C. (a)...
Evaluate Sc f(x,y)ds where is the curve y = x for 0 < x < 1 and the surface is f(x,y) = 1 + 9xy Select one: 14 a. 5 O a. V O b. O c. 18 13 O d. 1
2) (15 points) (a) (10 points) Compute the line integral s f(x,y) ds of the scalar function over the oriented curve. [C] 0 (5 points) How does your answer change if I reverse the orientation of Cl? f(0, y) = C): The curve parameterized by r(t) = t'i + t'j, t E (1.21