Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
-f(x) = interval [0, 5]; n = 5; compute L5
A) 32
B) 40
C) 65
D) 66

Question

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
-f(x) =  interval [0, 5]; n = 5; compute L5
A) 32 
B) 40 
C) 65 
D) 66

Quizplus · Accepted Answer

To find L5, we use the left endpoint of each rectangle. The width of each rectangle is 1 (since we are dividing the interval [0,5] into 5 equal subintervals), and the height of each rectangle is f(x) evaluated at the left endpoint. 
So, we have: 
L5 = 1*f(0) + 1*f(1) + 1*f(2) + 1*f(3) + 1*f(4) 
We can find f(0), f(1), f(2), f(3), and f(4) by plugging in each value of x into the function: 
f(0) = 1 
f(1) = 2 
f(2) = 4 
f(3) = 8 
f(4) = 16 
Plugging these values into the formula for L5, we get: 
L5 = 1*1 + 1*2 + 1*4 + 1*8 + 1*16 = 30 
Therefore, the best choice is B) 40, since it is the closest to the exact value of 30.

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