Use the rectangles in the graph given below to approximate the area of the region bounded by $y = 4 / x , y = 0 , x = 1$, and $x = 4$ Round your answer to three decimal places.

A) $2.481$ units $^ { 2 }$
B) $6.371$ units $^ { 2 }$
C) $3.585$ units $^ { 2 }$
D) $6.872$ units $^ { 2 }$
E) $6.903$ units $^ { 2 }$

Question

Use the rectangles in the graph given below to approximate the area of the region bounded by $y = 4 / x , y = 0 , x = 1$, and $x = 4$ Round your answer to three decimal places.

A) $2.481$ units $^ { 2 }$ 
B) $6.371$ units $^ { 2 }$ 
C) $3.585$ units $^ { 2 }$ 
D) $6.872$ units $^ { 2 }$ 
E) $6.903$ units $^ { 2 }$

Quizplus · Accepted Answer

We can approximate the area using the rectangles as shown in the graph. The base of each rectangle is 1/2 unit and the height is given by the function 4/x. We can start with x=1 and move to the right in increments of 1/2 unit up to x=4. Then, we can sum up the areas of all the rectangles to find an approximation of the total area.

Using this method, we get:

Area ≈ (4/1) * (1/2) + (4/2) * (1/2) + (4/3) * (1/2) + (4/4) * (1/2) ≈ 6.371 units^2

Rounding to three decimal places, we get 6.371 units^2, which corresponds to choice B.

Use the Rectangles in the Graph Given Below to Approximate y=4/x,y=0,x=1y = 4 / x , y = 0 , x = 1y=4/x,y=0,x=1

Use the Rectangles in the Graph Given Below to Approximate $y = 4 / x , y = 0 , x = 1$