128ahw8sum10 - MATH 128A SUMMER 2010 HOMEWORK 8 SOLUTION...

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MATH 128A, SUMMER 2010, HOMEWORK 8 SOLUTIONBENJAMIN JOHNSONHomework 8: Due Wednesday, July 214.8; 1d, 5d4.9; 1a, 85.1; 4b, 8a5.2; 2bsection 4.81 Use Algorithm 4.4 withn=m= 4 to approximate the following double integrals, andcompare the results to the exact answers.d.R1.51Rx0(x2+y)dy dxsolution:Algorithm 4.4 is just the composite Simpson’s rule applied to both integrals.Withn= 4, the rule isRbaf(x)dxb-a12f(a) +f(b) + 2f(a+b2) + 4(f(3a+b4) +f(a+3b4)) .Using this, we getZ1.
5 Use Algorithm 4.5 withn=m= 2 to approximate the integrals in Exercise 1, and comparethe results to those obtained in Exercise 1.d.R1.5Rx2+y)dy dxsolution:

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