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Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
5. Find the area of the surface obtained by rotating the curve y=Vx on the interval [0,1] around the y-axis. 6. Evaluate the integral dx (x+1)
2: Consider the curve with equation x2/3 + y2/3 = 1. -0.5 0 -0.51 a: Find the exact length of the curve. (Make good use of the symmetric property of the graph. ) b: Find the surface area of the solid obtained by rotating the curve about y-axis. (Watch out for the symmetric property of the graph.)
5. (12 pts.) Consider the region bounded by f(x) 4-2x and the x-axis on interval [-1, 4] Follow the steps to state the right Riemann Sum of the function f with n equal-length subintervals on [-, 4] (5 pts.) a. Xk= f(xa) (Substitute x into f and simplify.) Complete the right Riemann Sum (do not evaluate or simplify): -2 b. (1 pt.) lim R calculates NET AREA or TOTAL AREA. (Circle your choice.) Using the graph, shade the region bounded...
3. Find the area of the surface of revolution obtained by rotating the graph of y = 2x around the x-axis for the interval 0 Sxs To Give exact answer only.
problem 3 pls Problem 3. Consider the curve {> 1, y = 1/x}. Compute the length of the part of this curve lying to the left of the line x = a for any a > 1. Show that the length of the whole curve is thus infinite. Compute the area of the surface obtained by rotating this curve about about the x axis by computing the corresponding improper integral; it should be infinite. What is the area of the...
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.
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.
(a) Use a graphing utility to graph the curve represented by the following parametric 6. x y over the interval -2sts2. (b) Write an integral that represents -3t-1 the arc length of this curve over the interval -2sts2. (Do not attempt to evaluate this integral algebraically.) (c) Use the numerical integration capability of a graphing utility to approximate the value of this integral. Round your result to the nearest tenth. (Be careful with your notation, show orientation arrows on your...
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