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.

1)is not similar since corresponding sides are not in the same ratio

2)are similar since corresponding sides are in the same ratio and corresponding angles are equal

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