A record club has found that the marginal​ profit,

Upper P prime left parenthesis x right parenthesisP′(x)​,

in​ cents, is given by

Upper P prime left parenthesis x right parenthesis equals negative 0.0007 x cubed plus 0.39 x squared plus 67.4 xP′(x)=−0.0007x3+0.39x2+67.4x

for

x less than or equals 500x≤500​,

where x is the number of members currently enrolled in the club. Approximate the total profit when

300300

members are enrolled by computing the sum

Summation from i equals 1 to 6 Upper P prime left parenthesis x Subscript i Baseline right parenthesis Upper Delta x∑i=16P′xiΔx

with

Upper Delta x equals 50Δx=50.

010020030040050009,20018,40027,60036,80046,000Number of membersMarginal profit (in cents)

Upper P prime left parenthesis x right parenthesis equals negative 0.0007 x cubed plus 0.39 x squared plus 67.4 xP′(x)=−0.0007x3+0.39x2+67.4x

Upper II

IIII

IIIIII

IVIV

Upper VV

VIVI

A coordinate system has a horizontal axis labeled Number of members with ticks from 0 to 500 in increments of 50 and a vertical axis labeled Marginal profit (in cents) from 0 to 46000 in increments of 4600. A smooth curve labeled Upper P prime left parenthesis x right parenthesis equals negative 0.0007 x cubed plus 0.39 x squared plus 67.4 x generally rises from left to right. Six shaded 50-unit wide rectangles of different heights are spaced evenly along the horizontal axis from x equals 0 to x equals 300 with no gaps such that the bottom side coincides with the x-axis and the left corner of the top side is on the graph of the curve. The rectangles are labeled as follows from left to right: I, II, III, IV, V, VI.

Question content area bottom

Part 1

The total profit when

300300

members are enrolled is approximately

​$enter your response here.