1. Evaluate the following integralsA. f^2 0 (3x^3 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 0C. f (1/x+3)(dx)2. In a test run a new train travels along a straight-line track. Data obtainedFrom the speedometer indicate that the velocity of the train at any time t can beDescribed by the velocity functionV (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 beginningof the track so when t = 0 the integration constant C = 0.)3. The current circulation of a particular magazine is 3000 copies per week. TheEditor projects a growth rate ofG (t) = 4+5t^2/3Copies 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 xWidgets is found to beC (x) = 0.000009x^2 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 theCompany begins making a profit. (Hint: The revenue function is R(x) = $25x;
