+39 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
+23252 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
