A record club has found that the marginal​ profit, Upper P prime (x )​, in​ cents, is given by

Upper P prime (x )equals negative 0.0008 x cubed plus 0.20 x squared plus 46.8 x for x less than or equals 200​,

where x is the number of members currently enrolled in the club. Approximate the total profit when 120 members are enrolled by computing the sum

Summation from i equals 1 to 6 Upper P prime (x Subscript i Baseline )Upper Delta x with Upper Delta x equals 20.

Solution :

Given :

   for x ≤ 200

Total profit when 120 members are enrolled is :

     with

Using the left end points, we get,

The values of are : { 0, 20, 40, 60, 80, 100}

Therefore,

                        = 0

                          = 1009.6

                         =  2140.8

                         = 3355.2

                         = 4614.4

                           = 5880

= (0)(20) + (1009.6)(20) + (2140.8)(20) + (3355.2)(20) + (4614.4)(20) + (5880)(20)

= (20)( 0 + 1009.6 + 2140.8 + 3355.2 + 4614.4 + 5880)

= (20)(17,000)

= 340,000 cents

= 3400 dollars

Hence, the required total profit is 3400 dollars.

step-by-step explanation: