i eitn Letf(x) = cos(x2). Use (a) the Trapezoidal Rule and (b) the Midpoint Rule

Question

i eitn Letf(x) = cos(x2). Use (a) the Trapezoidal Rule and (b) the Midpoint Rule to approximate the integral )d with n 8. Give each answer correct to six decimal places. (c) Use the fact that f"(x)l S 6 on the interval [0, 1] to estimate the errors in the approximations from part (a). Give each answer correct to six decimal places. Error in TS = Error in M,- (d) Using the information in part (c) and the error formulas, how large do we have to choose n so that the approximations T, and Mn are accurate to within 0.00001? (Your answer must be a whole number) For 7, : n = For Mn : n =

Explanation / Answer

(a) T8 = 0.902333
(b) M8 = 0.905619

(c) Error in T8: 0.002191
Error in M8: -0.001095

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