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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.
2. Let a curve be parameterized by x = integral for the length of the curve. t3 – 9t, y=t+3 for 1 <t< 2. Set up (but do not evaluate) the
6. Let a curve be parameterized by x = t3 – 9t, y=t+3 for 1 st < 2. Find the xy coordinates of the points of horizontal tangency and vertical tangency.
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.
Find the arc length Lof x = f(t) = 9t + 14 y = g(t) = Si Vu – 81du where 0 < t < 16 =
Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts] Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y +22)j + xk
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
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) [5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral F. dr с where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
for b.
y= sin(x^2-3x+1)
og t par Set up, but do not evaluate, the integral required to compute the arc length of the curve cotr. y= 217from 0<x< /2. mense metied to compute Set up, but do not evaluate, the integral required to compute the surface area of the solid obtained by rotating the curve y=sin(x2 3x + 1), 0<x< 1 about the z-axis.