Determine these indefinite integrals (#1-#5)

1)x6dx

2)x21

3)x1/4dx

4)(x2+x1)dx

5)x4dx

6) A company determines that the marginal cost, C', of producing the xth unit of a product is given byC(x)=x32x

Find the total-cost function, C, assuming that C(x) is in dollars and that fixed costs are $7000.

7) A company determines that the marginal cost, C', of producing the xth unit of a product is given byC(x)=x3x

Find the total-cost function, C, assuming that C(x) is in dollars and that fixed costs are $6500.

8) The rate at which a machine operator's efficiency, E (expressed as a percentage), changes with respect to time t is given bydtdE=3010t where t is the number of hours the operator has been at work.

Find E(t), given that the operator's efficiency after working 2 hr is 72%; that is, E(2) = 72.

9) During 18 weeks from November 2009 to February 2010, the rate at which the number of cases of swine flu changed could be approximated byI=6.34t+141.6 where I is the total number of people who have contracted swine flu and t is time measured in weeks.

Estimate I(t), the total number who have contracted influenza by time t. Assume that I(0) = 1408.

10) Acceleration (a(t)) is the derivative of velocity (v(t)) which in turn is the derivative of the position function (s(t)). Given a(t) how can you recover velocity?