A function g(z) is defined in the interval [0, 1] on the z-axis as:

g(z) = { 2 if 0

Question

A function g(z) is defined in the interval [0, 1] on the z-axis as:

g(z) = { 2   if  0 <= z < 1/2
           { 3   if  1/2 <= z < 1
           { 2   if  z = 1

Which one of the following is the area under the curve for the interval [0, 1] on the z-axis?

A. 1/2  B. 3/4  C. 5/2  D. 3/2

Accepted Answer

Area under g(z) on [0, 1] = 5/2. Answer: C. 5/2. The function g(z) is piecewise constant: it equals 2 on [0, 1/2), equals 3 on [1/2, 1), and equals 2 at the single point z=1. The area under a piecewise constant function is simply the sum of (value * width) for each sub-interval. Since single points have zero width, the point z=1 contributes nothing.

A function g(z) is defined in the interval [0, 1] on the z-axis as: g(z) = { 2 if 0 <= z < 1/2 { 3 if 1/2 <= z < 1 { 2 if z = 1 Which one of the following is the area under the curve for the interval [0, 1] on the z-axis? A. 1/2 B. 3/4 C. 5/2 D. 3/2