The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R′(x)=(x+1)ln(x+1)R ′ (x)=(x+1)ln(x+1). Find the total revenue from the sale of the first 12 calculators. (Hint: In this exercise, it simplifies matters to write an antiderivative of x+1 as (x+8)2/2(x+8) 2 /2 rather than x2/2+x.)x 2 /2+x.)

Total revenue =  dollars

Step-by-step explanation:

Integrate with respect to .

∫ dx

Take

Differentiate with respect to

So,

∫

Use integration by parts: ∫f g dx = f∫ g dx-∫(∫g dx)f' dx

Therefore,

   ∫

=    ∫

Put

To find total revenue from the sale of the first 12 calculators, put

Total revenue =  dollars

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