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Clarence

  • one year ago

The radius, r, of a circular cell changes with time t. If r(t) = ln(t+2), then the change in the area of the cell, ΔA, that occurs between t=0 and t=1 is given by ΔA = ∫ 2π ln(t+2)/t+2 dt. True or False? :/

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  1. triciaal
    • one year ago
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    |dw:1444022894691:dw|

  2. FibonacciChick666
    • one year ago
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    So, what does an integral do?

  3. triciaal
    • one year ago
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    |dw:1444022983963:dw|

  4. triciaal
    • one year ago
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    |dw:1444023306505:dw|

  5. FibonacciChick666
    • one year ago
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    I assume your integral in the question is not indefinite? @Clarence

  6. clarence
    • one year ago
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    Yes, it's a definite integral, and I'm afraid I don't follow what triciaal has done... Sorry..

  7. FibonacciChick666
    • one year ago
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    so do integrals calculate area?

  8. clarence
    • one year ago
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    Yes?

  9. FibonacciChick666
    • one year ago
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    yea. by definition they do

  10. Jhannybean
    • one year ago
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    Think of derivatives as finding a small incremental section of an area, and integrals are integrating that small section to find the total area made of those small, incremental sections.

  11. FibonacciChick666
    • one year ago
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    so now, integrals calculate area under the curve. In this instance we need the area of a circle.

  12. FibonacciChick666
    • one year ago
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    |dw:1444024744065:dw|

  13. FibonacciChick666
    • one year ago
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    and what jhanny elegantly put is the concept I am trying to illustrate

  14. BAdhi
    • one year ago
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    I think this question is an application of the question you posted in the following link http://openstudy.com/study#/updates/561204cae4b06b089598f6ab where \(f(r) =2\pi r\) and \(g(t) = \ln(t+2)\)

  15. FibonacciChick666
    • one year ago
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    ^@BAdhi is correct. This is an application of the previous

  16. clarence
    • one year ago
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    So what do I actually have to do to solve this one? Just follow on from what I did previously?

  17. FibonacciChick666
    • one year ago
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    yep, see if it was applied correctly

  18. clarence
    • one year ago
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    Okay then, I'll try that thanks

  19. clarence
    • one year ago
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    After going through the same process that BAdhi did previously, it seems right to me

  20. FibonacciChick666
    • one year ago
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    I agree. Make sure you show your work with it on your paper :)

  21. clarence
    • one year ago
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    I will, thanks! :)

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