Question

Using both the Midpoint and Trapezoidal Rules with n subdivisions to approximate the integral of f(x) over the interval from a to b numerically, where f(x) is concave up on [a,b], then we would find?

Select one:

A. Midpoint overestimates, Trapezoid underestimates, Midpoint is better

B. Midpoint underestimates, Trapezoid overestimates, Midpoint is better

C. Midpoint overestimates, Trapezoid underestimates, Trapezoid is better

D. Midpoint underestimates, Trapezoid overestimates, Trapezoid is better

also,

If we used Gaussian Quadrature with 5 steps to approximate the integral of f(t) from -1 to 1 numerically, the degree of precision would be

Select one:

A. 5

B. 9

C. 7

D. 11

Answer 1

Using both the Midpoint and Trapezoidal Rules with n subdivisions to approximate the integral of f(x) over the interval from a to b numerically, where f(x) is concave up on [a,b], then

Midpoint underestimates, Trapezoid overestimates, Midpoint is better

Hence B is the right ans

If we used Gaussian Quadrature with 5 steps to approximate the integral of f(t) from -1 to 1 numerically, the degree of precision would be 7(c)

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