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

by | Aug 6, 2022 | Calculus homework help

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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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