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Choose the correct integral for finding the length of the curve given by the vector equation,...
Find the integral that represents the length of the parametric curve defined by x = e' –t, y = 2e2, 0 <t < 1. Select one: o al. Vre! – 1° +1 dt ObſVe4 – 2e + 2 de o af Vibe' + e² - 2te + 1² de O d. ſ' vroeken? + e= nº di o of Vie + 1 di O !!! Vet – e' + 1 de o ' viel + 1) di on I' v2e...
QUESTION 11 Consider the parametric equations, x =5e?' +2 and y = 1-5e27 Choose the integral that represents the exact length of the parametric curve on Ostsi S (102+(-102232 at • SV6587+22+(1–527 dt ost (+2)+(4+5) QUESTION 12 Which answer below would be a simpification of the correct integral in Question 117 Choose the best answer. QUESTION TO s 12 de of 10v7e2901 • S 15 +10e2' +5024) • $ 2007? 0 QUESTION 13 Use your answer from Question 12 to...
). Write the definite integral representing the length of the curve with parametric equations x=fl.y=g asi Sb. (a) [10]?dt [1+S'(12 de afv+00F4 va ant.5(e) de 109/1+ [8°(6)de in jur(e) +3'(6)]? de (0) $(1+[*()}) de miVirof +8"(t)?de
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...
a) Find the length of the curve traced by the given vector function on the indicated interval: r(t)e' costie' sin tj+e'k 0<t<In2 b) Find the gradient of the scalar function f 6xyz + 2x+ xz at (1, 1, -1) c) Find the curl of the given vector field: F(x, y,z) 4xyi + (2x2 +2yz)j+(3z2+y2)k
4. (18 points) Verify Stokes' Theorem in finding the counterclockwise circulation of the vector field, F - (r-i + (42)j + (r) k around the curve, C, where C is the triangular path determined by the points (6,0,0),(0,-4,0),and (0,0,10) . (i.e. calculate the circulation % F.iF directly, and then by using Stokes' Theorem and doing a surface integral.) Which way was easier? (Hint: You will need to find the equation of the plane that goes through these three points.) 4....
Let C be the curve with parametrization 7 (t) = 8sin(t) 7 - 8cos(t)j + (15t-10) where 0 sts2. Which of the following is equal to dř in the line integral (3.dñ of a vector field F(x, y, z) along C. Select one: a. di = 17dt b. dr = [8cos(t)7 +8sin(t)] +15K ]dt c. di = 289dt d. dň = [8sin(t) 7 – 8cos(t)] +15K ]dt e. di = [8cos(1)7 - 8sin(t)] + 15% ]dt
Find the arc length parameter along the curve from the point where t=0 by evaluating the integral s | |vIdT. Then find the length of 0 the indicated portion of the curve. The arc length parameter is s(t) (Type an exact answer, using radicals as needed.) Find T, N, and k for the plane curve r(t) (2t+9) i+ (5-t2) j T(t)= (Type exact answers, using radicals as needed.) (Type exact answers, using radicals as needed.) Find the arc length parameter...
ili Quot 12.3.14 Find the arc length parameter along the curve from the point where t = 0 by evaluating the integral s - Sivce)| dr. Then find the length of the indicated portion of the curve. -jwel de r(t)- (5 + 3)i + (4 +31)j + (2-7)k, - 1sts The arc length parameter is s(t)=0 (Type an exact answer, using radicals as needed.)
Problem 2: (0.2 point) The position vector, infeet, of an object follows a space curve defined by: r =e i[sin(t)+cos(t)j+cos(2t)k where t is time in seconds. Find the arc length of this space curve between 0 and 2 seconds 0.5- Be sure to clearly show the arc length integral Then use the trapezoidal rule with n 40 to approximate the arc length. Give your answer out to 3 decimal places. 0- You may use the tool of your choice to...