Which of the following integrals represents the length of the parametric curve x = 1+e', y=t,...
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...
(6pts) Consider the curve given by the parametric equations x = cosh(4t) and y = 4t + 2 Find the length of the curve for 0 <t<1 M Length =
Consider the curve X = 42 y=ť, 0 <t<1 Setup the integral for the area of the surface obtained by rotating the curve about 27 (2+4 + 3t") dt [ 26 (28 + 3t) dt 2*t* 4 +01+ dt 27tº /2 + 3* dt [ 2013 (4+9t? dt
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
Question 15 < > Find the length of the curve for the following parametric equations for 2 <t < 10. Find its exact value, no decimals. r(t) = e' - 36 ly(t) = 2461/2 Length =
Consider: 5x2-y’ds, C:r(t)=<2t, – 1), te[0,11 Which one of the following "regular" integrals represents the above line integral. 312dt 1 oors ! *52-2 + 14t V5S 3+2+2t - 1dt Ос. 1 d. f 31² + 28-1dt 1 -15% 312 +2t - 1dt
1 1 a) Compute the length of the curve y = Inx, for 1 < x < 2. b) Compute the area of the surface obtained when rotating the curve in question a) about the y-axis, for 1 < x < 2.
3. Suppose the curve x = = t3 – 9t, y=t+ 3 for 1 <t< 2 is rotated about the x-axis. Set up (but do not evaluate) the integral for the surface area that is generated.
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
Find the length od the curve C defined by х = t2/2 - Int, y = 2t for 1 <t <2.