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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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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;

Tags probelms integrals widgets function train cost circulation position company producing daily velocity copies week subscript power track 0009x 0000009x2 unit dollars produce measured marginal years e2xx2 manufactures fixed integrals costs making begins

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Integrals Probelms Solution

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Tutorial Preview …Evaluate xxx…
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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