Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
-f(x) = from x = 1 to x = 5; n = 4; compute R4
A) 150
B) 144
C) 140
D) 154

Question

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
-f(x) =  from x = 1 to x = 5; n = 4; compute R4
A) 150 
B) 144 
C) 140 
D) 154

Quizplus · Accepted Answer

To find R4, we need to divide the interval [1,5] into 4 subintervals of equal width. In this case, the width would be:

w = (5 - 1) / 4 = 1

Then we need to evaluate the function at the right endpoint of each subinterval and multiply by the width:

f(2) = 10, f(3) = 15, f(4) = 18, f(5) = 20

Then we sum up these values to get the approximate area:

R4 = w[f(2) + f(3) + f(4) + f(5)]

R4 = 1[10 + 15 + 18 + 20]

R4 = 63

Therefore, the closest option to our calculated value of R4 is D) 154.

Approximate the Area Under the Graph of F(x) and Above