(10 points each) Consider the curve y = r² from the point (1,1) to the point...
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.
1. For the curve defined by y=725 - r from x = 0 to x = 4 Set-up the integral that finds the length of the arc formed by the curve. You do not need to simplify the expression undemeath the radical. Do not integrate! b. [6 pts) Set-up the integral that finds the surface area of the solid generated by revolving the curve about the x-axis, You do not need to simplify the expression underneath the radical. Do not...
7. (10 points) Consider the linear path "C" in the xy-plane from the point (1,1) to the point (2,3). (a) Find an appropriate vector valued function r(t) along with an appropriate interval a <t<b which describes the path C. (b) Evaluate the line integral 2xy ds where C is the curve you found above.
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...
36a and 37
12:41 - A A) a a lies between the points (0,0) and (1,1). If your CAS has trouble evaluating the integral, make a substitution that changes the integral into one that the CAS can evaluate. 33. Sketch the curve with equation x2/3 + y2/3 = 1 and use symmetry to find its length. 34. (a) Sketch the curvey - x (b) Use Formulas 3 and 4 to set up two integrals for the are length from (0,0)...
Express the Arc Length of the given curve on the
specified interval as a definite integral. Don't evaluate, just set
it up.
y=ez) on (0.2]
a) Set up an integral that gives the length of the curve y^ 2 + y = 2x from the point (1, 1) to (3, 2). Do NOT evaluate the integral. b) Let R be the region bounded by y = 1 and y = cos x between x = 0 and x = 2π. Set up an integral that gives the volume of the solid formed by rotating R about the line x = −π. See the figure below....
Consider the region R between the curves y = and y +7. (a) Sketch this region, making sure to find and label all points of intersection. (You are not required to simplify expressions for these if they end up being complicated. (b) Set up an integral for the area of this region using vertical rectangles. Do not evaluate the integral, just set it up. (C) (Harder! Do this problem last.) Set up an integral or integrals for the area of...
B Consider the shaded region bounded by y=x2 – 4 and y= 3x + 6 (see above). Note that the r-axis and y-axis are not drawn to the same scale. (a) Find the coordinates of the points A, B, and C. Remember to show all work. (b) Set up but do not evaluate an integral (or integrals) in terms of r that represent(s) the area of the region. That is, your final answer should be a definite integral (or integrals)....
Consider the curve y = 4 + (2x - 1)3/2 on the Interval 0.5 5 * 5 1. The graph is shown below. 4.5 0.4 0.6 0.8 1 1.2 [4] (a) Find the arc length of this curve on the interval 0.5 SX S1. [3] (b) Set up but do not evaluate an integral for the surface area obtained by rotating this curve on the interval 0.5 SXS l about the x-axis.