Posted by **Roland** on Wednesday, April 24, 2013 at 11:36pm.

Part I

The change in annual revenue in thousands of dollars for the Ozark Zip Line Corporation has been modeled by the function.

R(x) = 8.2x^2 + 23.1x

where x is the number of years after 2000. To find the total revenue gained between the years 2002 and 2005, start by choosing a constant (C)530

Part II

Build the definite integral that is used to find the total revenue gained between the years 2002 and 2005

Part III

Apply the power rule to integrate R(x) over the given interval, and round your answer to the nearest whole tens of dollars.

- Calculus -
**Reiny**, Thursday, April 25, 2013 at 8:02am
let the annual revenue be A(x)

then

A ' (x) = R(x) = 8.2x^2 + 23.1x

A(x) = (1/3)(8.2)x^3 + (23.1/2)x^2 + C

= (41/15) x^3 + (23/20)x^2 + c

at year 2000, t = 0 and c = 530

at year 2002, t = 2

A(2) = (41/15)(8) + (23/20)(4) + 530

A(5) = (41/15)(125) + (23/20)(25) + 530

A(5) - A(2)

= [ (41/15)(125) + (23/20)(25) + 530 ] - [(41/15)(8) + (23/20)(4) + 530]

= $ 343.95

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