a.) Use Simpson\'s Rule with n = 10 to estimate the arc length of the curve. Com

ID: 3342219 • Letter: A

Question

a.) Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.)

y=xe^-x + 2 0 less than or equal x less than or equal to 5

b.)Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.)

y=xlnx+5 1 less than or equal x less than or equal to 3

Explanation / Answer

See here for a tutorial on how to find arc length: http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx

a.)
y' = e^-x - xe^-x
%u222B%u221A(1 + (e^-x - xe^-x)^2 ) dx from 0 to 5...
%u222B%u221A(1 + e^-2x - xe^-2x) ) dx ....

f(x) = %u221A(1 + e^(-2x) - xe^(-2x))

(applying Simpson's rule) 0.5/3 [ f(0) + 4f(0.5) + 2f(1) + 4f(1.5) + 2f(2)+ 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4) + 4f(4.5) + f(5) ]
= 1/6 [ (1.4142) + 4(1.0881) + 2(1.0000) + 4(0.9875) + 2(0.9908)+ 4(0.9949) + 2(0.9975) + 4(0.9989) + 2(0.9995) + 4(0.9998) + (0.9999) ]
= 5.11

Using calculator: http://www.wolframalpha.com/input/?i=arc%20length%20xe%5E-x%20from%200%20to%205

b.)

Arc length is

%u222B%u221A(1 + (1+ln x)^2) dx from 0 to 3

1/15(58.044271)

= 3.870 using Simpson's rule

Using calculator: http://www.wolframalpha.com/input/?i=arc+length+xlnx%2B5+from+1+to+3