1. Evaluate the integral ∫x5(x^6−10)^47dx by making the substitution u=x^6−10.

1.  Evaluate the integral
∫x5(x^6−10)^47dx
by making the substitution u=x^6−10.

=_+C

2. Evaluate the indefinite integral.

∫7dx/xln(8x)

=_  + C

3.  Evaluate the indefinite integral.

∫x^8e^x^9dx

=_+C

4.  Evaluate the indefinite integral.

∫x4(15+x^5)^1/2dx
=_+C

5.  Evaluate the indefinite integral.

∫4/(t+5)^8 dt

=_+C

6.  Evaluate the indefinite integral:

 ∫x/x^2+4 dx

=_+C

7.   A cell culture contains 4 thousand cells, and is growing at a rate of r(t)=11e^0.24t thousand cells per hour.

Find the total cell count after 4 hours. Give your answer accurate to at least 2 decimal places.

 _ thousand cells 

8.  Use integration by parts to evaluate the integral:
∫2te^tdt = 

9.  ∫4xe^7xdx =    + C 

10.  Use integration by parts to evaluate the integral:

∫ln(7x−1)dx

11.  Use integration by parts to evaluate the integral:

∫ln(z)√z^13dz

12.  Find ∫4x/3x+2dx

=_+C

13.  Integrate: ∫x/(x^4+25)^1/2dx

 =_ + C 

14.  Find ∫(−2x^2+3/x−1/x^4+4√x)dx

 =_ + C 

15.  Find ∫(x+4)(x−6)dx

  =_ + C 

16.  The traffic flow rate (cars per hour) across an intersection is r(t)=400+700t−270t2r(t)=400+700t-270t^2, where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 7 am?

  _cars 

17.  A company’s marginal cost function is 17/√x where x is the number of units.

Find the total cost of the first 36 units (of increasing production from x=0 to x=36)

Total cost: $

 

 

 

 

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