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: $