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Total Revenue

  1. May 3, 2012 #1
    1. The problem statement, all variables and given/known data
    According to data, the marginal revenue of a product(in billions of dollars per year) is approximated by 3.96+.01x+.0012x^2, where x=0 corresponds to 1980. What was the total revenue from the beginning of 1996 through the end of 2002?


    2. Relevant equations



    3. The attempt at a solution
    ∫23 on top, 17 on bottom (3.96+.01x+.012^2)=(3.96.02x^2+.004x^3)|23 on top, 17 on bottom
    63.208-29.392=33.816
     
  2. jcsd
  3. May 3, 2012 #2

    Mark44

    Staff: Mentor

    Do you have a question?
     
  4. May 3, 2012 #3
    yes the answer i got 33.816 was wrong, can you help with the solution
     
  5. May 3, 2012 #4

    Mark44

    Staff: Mentor

    The beginning of 1996 corresponds with x = 16, not 17. The other limit of integration, 23, looks OK.

    Also, your integration is wrong.

    $$\int cx^n dx = \frac{c}{n+1}x^{n+1}$$
    I omitted the constant of integration since you're working with a definite integral.
    What you're doing looks like you are differentiating, not integrating.
     
  6. May 3, 2012 #5
    ok im still confused
     
  7. May 3, 2012 #6

    Mark44

    Staff: Mentor

    About what?
     
  8. May 3, 2012 #7

    Mark44

    Staff: Mentor

    For the integration part, the integrand is 3.96+.01x+.012^2 (the last term should be .012x^2).

    The antiderivative you showed is 3.96.02x^2+.004x^3.

    1. In the antiderivative you have two terms munged together (3.96.02x^2).
    2. The antiderivative of 3.96 is NOT 3.96.
    3. The antiderivative of .01x is NOT .02x^2.
     
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