06 Aug 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
1. Evaluate the integral
by making the substitution u=x^6−10.
2. Evaluate the indefinite integral.
=_ + C
3. Evaluate the indefinite integral.
4. Evaluate the indefinite integral.
5. Evaluate the indefinite integral.
6. Evaluate the indefinite integral:
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:
9. ∫4xe^7xdx = + C
10. Use integration by parts to evaluate the integral:
11. Use integration by parts to evaluate the integral:
12. Find ∫4x/3x+2dx
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?
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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