Apply Simpson’s Rule to the following integrals. It is easiest to obtain the Simpson’s Rule approximations from the Trapezoid Rule approximations. Make a table similar to Table 7.8 showing the approximations and errors for n = 4, 8, 16, and 32. The exact values of the integrals are given for computing the error.

Data from Table 7.8

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Error in T(n) Error in S(n) S(n) T(n) 0.25904504019141 п 4 0.00520 0.26423805546593 0.26293980164730 0.00130 0.00000306 16 0.26391564480235 0.26424092585404 0.000325 0.000000192 0.26424110566291 32 0.26415974044777 0.0000814 0.0000000120 0.0000203 64 0.26422077279247 0.26424111690738 0.000000000750 128 0.26423603140581 0.26424111761026 0.00000509 0.0000000000469 3e 3* dx = 1 – e 18 = 1.000000