Homework SourseConsider the curve yxsinx 0
Consider the curve
y=x+sinx , 0<=x<=2pi
(a) Compute the lengths of inscribed polygons with n = 1, 2, and 4 sides. (In other words, divide [0,2pi] up into 1,2, and 4 equal segments, and draw line segments between those values on the graph. Then compute the length of the polygonal curve you drew)
Length for n = 1:
Length for n = 2:
Length for n = 4:
(b) Use a calculator or a computer algebra system to find the length of the curve to four decimal places.
Length of curve =
y=x+sinx , 0<=x<=2pi
(a) Compute the lengths of inscribed polygons with n = 1, 2, and 4 sides. (In other words, divide [0,2pi] up into 1,2, and 4 equal segments, and draw line segments between those values on the graph. Then compute the length of the polygonal curve you drew)
Length for n = 1:
Length for n = 2:
Length for n = 4:
(b) Use a calculator or a computer algebra system to find the length of the curve to four decimal places.
Length of curve =
Solution
<p>dy/dx=1+cos x<br />so ds=sqrt[(1+(dy/dx)^2)*dx]<br />length=<img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-2012521141386347320569838156799519.gif" alt="" align="absmiddle" /></p>![Consider the curve y=x+sinx , 0<=x<=2pi (a) Compute the lengths of inscribed polygons with n = 1, 2, and 4 sides. (In other words, divide [0,2pi] up into](/WebImages/29/consider-the-curve-yxsinx-0-1078697-1761566140-0.webp "Consider the curve y=x+sinx , 0<=x<=2pi (a) Compute the lengths of inscribed polygons with n = 1, 2, and 4 sides. (In other words, divide [0,2pi] up into")
