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.
5. Let a curve be parameterized by x = t3 + 9t, y=t+3 for 1 <t < 2. Set up and evaluate the integral for the area between the curve and the x-axis. Note that x(t) is different from the other problems.
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.
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.
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
3. (6 points) Consider the curve y = 2 - 2.22 restricted to the first quadrant. (a) Set up a definite integral that gives the length of this curve. Do NOT evaluate the integral (b) Set up a definite integral that gives the surface area of the solid generated by rotating the curve about the x-axis. Do NOT evaluate the integral.
Find the arc length Lof x = f(t) = 9t + 14 y = g(t) = Si Vu – 81du where 0 < t < 16 =
(1 point) Find the area of the surface obtained by rotating the curve y = yæ about y-axis for 1 < y < 2. Area:
Find the exact length of the curve. x = t 2 + t' y = In(2 + t), 0<t< 5 1.2986 Need Help? Read It Watch It Talk to a Tutor