Consider the following table. x f(x) x f(x) 0.0 6.7 2.0 7.6 0.4 6.2 2.4 8.4...

 

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Consider the following table. x f(x) x f(x) 0.0 6.7 2.0 7.6 0.4 6.2 2.4 8.4 0.8 6.6 2.8 8.9 1.2 6.8 3.2 8.3 1.6 6.5 (a) Use the midpoint rule with n = 4 and the given data to estimate the value of the following integral. (Round your answer to two decimal places.) 3. f(x f(x) dx (b) If it is known that -4 < f"(x) 2 for all x, estimate the error involved in the approximation in part (a) using the smallest possible value for K according to this theorem. (Round your answer to four decimal places.) IEM S Consider the following table. x f(x) x f(x) 0.0 6.7 2.0 7.6 0.4 6.2 2.4 8.4 0.8 6.6 2.8 8.9 1.2 6.8 3.2 8.3 1.6 6.5 (a) Use the midpoint rule with n = 4 and the given data to estimate the value of the following integral. (Round your answer to two decimal places.) 3. f(x f(x) dx (b) If it is known that -4 < f"(x) 2 for all x, estimate the error involved in the approximation in part (a) using the smallest possible value for K according to this theorem. (Round your answer to four decimal places.) IEM S