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Find the approximate area between the curve f(x)=-2x + 32x + 5 and the x-axis on the interval (0,16] using 4 rectangles. Use the left endpoint of each rectangle to determine the height.

 

A.2304 square units

B.576 square units

C.320 square units

D. 1360 square units

 Jun 9, 2020
 #1
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I'm assuming that the function is  f(x)  =  -2x2 + 32x + 5.

 

To divide the interval (0,16] into four rectangles, the dividing points are:  0,  4,  8,  12,  16

The left-hand endpoints are: 0, 4, 8, and 12.

f(0)  =  5

f(4)  =  101

f(8)  =  133

f(12)  =  101

 

To find the areas of the rectangles, multiply each height by its width (which is 4).

 

5x4  +  101x4  +  133x4  +  101x4  =  1360

 Jun 9, 2020

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