  Use Simpson's rule to approximate the following integral and compare your1.result to the exact value of the integral.6x21dx

Question help_outlineImage TranscriptioncloseUse Simpson's rule to approximate the following integral and compare your 1. result to the exact value of the integral. 6x21dx fullscreen
Step 1

The integral is given as help_outlineImage Transcriptionclose(2x -6x +1) First simply integrate it 2 4 6 + 3 =8-16 2 =-6 Thus, the exact result of definite integral is-6 fullscreen
Step 2

For Simpson’s rule, the area is approximated within two intervals help_outlineImage Transcriptioncloseand x,x Ax That is, A 3 )(%.) Forn sub intervals, the integral becomes b-a f(a)+4f(x) + 2f (x, )+4f(x)+ 2f(x.) ...+f(x)4(x)+ f(b) 3n+. fullscreen
Step 3

Obtain the width of eac... help_outlineImage Transcriptioncloseb-a 2-0 n 1 =_ 2 [0,0.5].[0.5.1],11.5] and [1.5,2]. Thus, the subintervals are fullscreen

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