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# Integrals Probelms

Question # 00005485
Subject: Mathematics
Due on: 12/16/2013
Posted On: 12/15/2013 11:22 PM

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Question

1. Evaluate the following integrals

A. f^2 0 (3x^3 āx^2 +2) dx this is (f) with subscript of 0 and (f) to the power of 2.

B. f^1 0 (e^(2x)-x^2) dx this is (f) to the power of 1 and (f) with a subscript of 0

C. f (1/x+3)(dx)

2. In a test run, a new train travels along a straight-line track. Data obtained
From the speedometer, indicate that the velocity of the train at any time t can be
Described by the velocity function

V (t) =8t (0?t?30)

a. Find the position function of the train.
b. Find the position after 3 seconds. (Note: the train starts from the beginning
of the track so when t = 0, the integration constant, C = 0.)

3. The current circulation of a particular magazine is 3,000 copies per week. The
Editor projects a growth rate of

G (t) = 4+5t^2/3

Copies per week after t weeks.

a. Find the circulation function based on this projection.
b. Find the circulation in 2 years.

4. A company manufactures widgets. The daily marginal cost to produce x
Widgets is found to be

Cā(x) = 0.000009x^2 ā 0.009x + 8

(Measured in dollars per unit). The daily fixed costs are found to be \$120.

a. Use this information to get a general cost function for producing widgets.
b. Find the total cost of producing the first 500 widgets.
c. If you sell the widgets for \$25 each, how many will need to be sold before the
Company begins making a profit. (Hint: The revenue function is R(x) = \$25x;
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#### Integrals Probelms Solution

Tutorial # 00005296
Posted On: 12/15/2013 11:27 PM
Posted By:
expertden
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Tutorial Preview …Evaluate xxx…
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Integrals_Probelms_Solution.docx (445.31 KB)
Preview: function xx the xxxxx b Find xxx position after x seconds xxxxxx xxx train xxxxxx from the xxxxxxxxx of the xxxxx so xxxx x = xx the integration xxxxxxxxx C = x ) xxxx x = xx the position xxxxxxxx becomes After x seconds, xxx xxxxxxxx is: x The current xxxxxxxxxxx of a xxxxxxxxxx magazine xx xxxxx copies xxx week The xxxxxx projects a xxxxxx rate xx x (t) x 4+5t^2/3Copies per.....
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