Let C be the graph of f(x) = sinx, 0 <x<pi
a. set up an integral that computes the arc length of C
b. use Simpson's rule with n=6 to approximate the arc length
c. set up an integral that computes the surface area of surface that results by rotating c about the x-axis
d. use Simpson's rule with n =6 to approximate the surface area of the surface in part c
e. set up an integral that computes the surface area of the surface that results by rotating C about the line y =1
f. use Simpsons rule with n =6 to approximate the surface area of the surface in part e.
Let C be the graph of f(x) = sinx, 0 <x<pi a. set up an integral that computes the arc leng...
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...
Set up (but do not evaluate) an integral to determine the arc length of the curve y = x2 from x = 0 to x = 2. 3 (12pt) TT TT Paragraph Arial %D9 ==== T TY TO ABC Evaluate the integral found in the previous question using Simpson's rule with n = 4. Round your answer to 4 decimal places
1. Let C be the set of points which satisfy y. Write down an integral which finds the distance from (1, 1) to (2,22/5) along the curve. Do not directly evaluate this integral. Instead use Simpson's rule with n 4 to approximate the length.
1. Let C be the set of points which satisfy y. Write down an integral which finds the distance from (1, 1) to (2,22/5) along the curve. Do not directly evaluate this integral. Instead use Simpson's...
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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.
1. The natural logarithm of (x > 0) can be computed using In(x) dt. Use (a) the mid-point rule, (b) trapezoidal rule, and (c) Simpson's Rule with N 6 subdivisions to approximate In(7) To aid the computation process it might be useful to set up a table containing values for xư x-f(x), f(x), and the weightings for the each of the numerical techniques. For example, i | zi | f(zi) | ที่ | f(r) | midpoint | trapezoidal Simpson's 1...
10 Let C be the portion of the curve y-sinx for 0SxS T. Write down an integral representing the area of the surface obtained by revolving C about the indicated line. (a) the x-axis (c) the line x-4 (e) the line y 1 (b) the y-axis (d) the line x--1 (f) the line y -1
10 Let C be the portion of the curve y-sinx for 0SxS T. Write down an integral representing the area of the surface obtained by...
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c) Sketch the graph and set up the integral to find the volume of the solid obtained by rotating Pabout the line y- 1. Vertical or Horizontal slicing? Disk or a Washer? V.[[4ωά α V-[Λωω or Area of a slice A- Volume V d) Sketch the graph and set up the integral to find the volume of the solid obtained by rotating about the y - axis. Vertical or Horizontal slicing? Disk...
Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.) y = x + sqrt(x) ,4 ≤ x ≤ 5
a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically.
a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically.
10. Trapezoidal Rule is used to approximate the integral f(a) dx using 1- (yo +2y1 + 2y2 + x-na b-a + 2yn-1 +%),where Use this approximation technique to estimate the area under the curve y = sinx over。 a. π with n 4 partitions. x A 0 B: @ Δy B-A b. The error formula for the trapezoidal rule is RSL (12ba)1 where cischosen on the interval [a, b] to maximize lf" (c)l. Use this to compute the error bound...