Question

(a) Use the Midpoint Rule, with n = 4, to approximate the integral ??? 7e??² dx. M? = 6.202947 (Round your answers to six decimal places.) (b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the TI83/84 or 2ND 7 on the TI- 89. ??? 7e??² dx = 6.20359 . (c) The error involved in the approximation of part (a) is E_M = ??? 7e??² dx - M? = 0.000643 . (d) The second derivative f''(x) = -14xe^(-x2) . The value of K = max |f''(x)| on the interval [0, 4] = 14 . (e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |E_M| ? K(b-a)³/24n² = 1.94 (where a and b are the lower and upper limits of integration, n the number of partitions used in part a). (f) Find the smallest number of partitions n so that the approximation M_n to the integral is guaranteed to be accurate to within 0.001. n =

          (a) Use the Midpoint Rule, with n = 4, to approximate the integral ??? 7e??² dx.
M? = 6.202947 (Round your answers to six decimal places.)

(b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the TI83/84 or 2ND 7 on the TI- 89. ??? 7e??² dx = 6.20359 .

(c) The error involved in the approximation of part (a) is
E_M = ??? 7e??² dx - M? = 0.000643 .

(d) The second derivative f''(x) = -14xe^(-x2) .
The value of K = max |f''(x)| on the interval [0, 4] = 14 .

(e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |E_M| ? K(b-a)³/24n² =
1.94 (where a and b are the lower and upper limits of integration, n the number of partitions used in part a).

(f) Find the smallest number of partitions n so that the approximation M_n to the integral is guaranteed to be accurate to within 0.001. n =

(a) Use the Midpoint Rule, with n = 4, to approximate the integral ??? 7e??² dx.
M? = 6.202947 (Round your answers to six decimal places.)

(b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the TI83/84 or 2ND 7 on the TI- 89. ??? 7e??² dx = 6.20359 .

(c) The error involved in the approximation of part (a) is
EM = ??? 7e??² dx - M? = 0.000643 .

(d) The second derivative f”(x) = -14xe^(-x2) .
The value of K = max |f”(x)| on the interval [0, 4] = 14 .

(e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |EM| ? K(b-a)³/24n² =
1.94 (where a and b are the lower and upper limits of integration, n the number of partitions used in part a).

(f) Find the smallest number of partitions n so that the approximation Mn to the integral is guaranteed to be accurate to within 0.001. n =

Added by Robert N.

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