Find the arc length for the following curves a. y2 = 4(x + 4), b. x...
1) Find the arc length for the following curves. a. y2 = 4(x + 4)3, b. x= 0<x<2 1 sys2 + 4y2 2) Find the surface area resulting from the rotation of the curve about X axis a. 9x = y2 + 18, b. y = V1 + 4x, 2<x< 6 1<x<5 3) Find the surface area resulting from the rotation of the curve about th Y axis. a, y = 1- x2 0 SX S1
(2 points) Find the exact length of the curve y = In(sin(x)) for #/6 <</2. Arc Length Hint: You will need to use the fact that ſesc(x) dx = In|csc() - cot(3) + C.
Find the arc length Lof x = f(t) = 9t + 14 y = g(t) = Si Vu – 81du where 0 < t < 16 =
4. Determine the integral which computes the arc length of the curve y = sin(x) with 0 < x <. TT A '1 + sin2(a)dx so $." .TT B 1 + cos2(x)dx С [* V1 – cos? (7)dx D| None of the above.
Find the arc length of the following curve. 1 sece 0<O<* a is a constant O a*r-1 O None of the given choices O a?7 - 1 O at O a??
2. (10 points) Find the arc length of the following paths. (The length of the path e(t) for to st<t is L = S ||'(t)||dt) (a) (5 points) c(t) = (t +1, 24243/2, {{2) for 1sts2
Problem 4, Find, for 0-x-π, the arc-length of the segment of the curve R(t) = (2 cos t-cos 2t, 2 sin t-sin 2t) corresponding to 0< t < r
Find the maximum and minimum of e-x2–v? (x² + 2y) on the disk x2 + y2 < 2.
4. Find the length of the curve x 1 f(x)= 12 +-, 1<x<4. х
Question 2 QUESTION 2. MULTIPLE CHOICE. Find the exact arc length of the curve y on the interval 0 << 7. Show your work on a sheet of paper and clearly label it QUESTION 2. Make sure your work is in numerical order by question number 1024 27 128 27 1022 27 170 9 512 27