Suppose you want to use the Midpoint Rule with n = 4 and equal-length subintervals to approximate $\int _ { 1 } ^ { 6 } e ^ { - x } d x$ ? What are the sample points you would use to compute the heights of the rectangles used in this approximation

A) $\{ 1,7 / 2,6 \}$
B) $\{ 1,13 / 8,23 / 8,33 / 8,43 / 8,6 \}$
C) $\{ 13 / 8,23 / 8,33 / 8,43 / 8 \}$
D) $\{ 9 / 4,19 / 4 \}$
E) $\{ 1,9 / 4,7 / 2,19 / 4,6 \}$

Question

Suppose you want to use the Midpoint Rule with n = 4 and equal-length subintervals to approximate

\int _ { 1 } ^ { 6 } e ^ { - x } d x

? What are the sample points you would use to compute the heights of the rectangles used in this approximation

A) $\{ 1,7 / 2,6 \}$
B) $\{ 1,13 / 8,23 / 8,33 / 8,43 / 8,6 \}$
C) $\{ 13 / 8,23 / 8,33 / 8,43 / 8 \}$
D) $\{ 9 / 4,19 / 4 \}$
E) $\{ 1,9 / 4,7 / 2,19 / 4,6 \}$

Quizplus · Accepted Answer

The interval [1, 6] is divided into 4 equal-length subintervals: [1, 2.25], [2.25, 3.5], [3.5, 4.75], [4.75, 6]. The midpoint of each subinterval, used as the sample point, is $13/8$ (1.625), $23/8$ (2.875), $33/8$ (4.125), and $43/8$ (5.375) respectively.

Suppose You Want to Use the Midpoint Rule with N ∫16e−xdx\int _ { 1 } ^ { 6 } e ^ { - x } d x∫16​e−xdx

Suppose You Want to Use the Midpoint Rule with N $\int _ { 1 } ^ { 6 } e ^ { - x } d x$