Concept explainers
Evaluating a Line
(a).
(b).
Evaluating a Line Integral for Different Parametrizations In Exercises 1–4, show that the value of
(a).
(b).
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Calculus: Early Transcendental Functions
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- Fur Find the area of the surface. Syr The helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v) i + u sin(v) j + v k, 0 s u s 1, 0 s vs 5x.arrow_forwardQ1,- A- Locate the centroid (X only) of the shaded area y=12 -3x 3 m Fig. L.A 2 marrow_forwarda) A three dimensional motion of an object is given by the vector function r(t) = 4 cos t i+ 4 sin tj+5 k. Sketch the motion of the object when 0arrow_forwardFirnd the area of the surface of the half cylinder {(r,0,z): r=6, 0s0S1, 0SzS5} using a parametric description of the surface. Set up the integral for the surface area using the parameterization u=0 and v=z. !! S SO du dv (Type an exact answers, using x as needed.) The surface area is (Type an exact answer, using x as needed.)arrow_forwardLet S be the surface parametrized by r (u, v) 0 ≤ ≤ 27. What shape is S? a sphere part of a sphere an ellipsoid a cone the lateral surface of a cylinder a plane a rectangle in R³ a disk in R³ U COS V u sin v 4- - U for (u, v) in the rectangle defined by 0 ≤ u ≤ 2 andarrow_forwardulus III |Uni Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along CoS the positively oriented curve C, where C is the rectangle with vertices(0,0), (4, 0), (4, 2) and (0, 2).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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