Evaluate the following integrals
f^2 0 (3x^3 –x^2 +2) dx this is (f) with subscript of 0 and (f) to the power of 2.
f^1 0 (e^(2x)-x^2) dx this is (f) to the power of 1 and (f) with a subscript of 0
In a test run, a new train travels along a straight-line track.
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)
Find the position function of the train.
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.
The current circulation of a particular magazine is 3,000 copies per week.
Editor projects a growth rate of
G (t) = 4+5t^2/3
Copies per week after t weeks.
Find the circulation function based on this projection.
Find the circulation in 2 years.
A company manufactures widgets.
The daily marginal cost to produce x
Widgets is found to be
C’(x) = 0.
000009x^2 – 0.
009x + 8
(Measured in dollars per unit).
The daily fixed costs are found to be $120.
Use this information to get a general cost function for producing widgets.
Find the total cost of producing the first 500 widgets.
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;