## anonymous 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? :/

1. triciaal

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2. FibonacciChick666

So, what does an integral do?

3. triciaal

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4. triciaal

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5. FibonacciChick666

I assume your integral in the question is not indefinite? @Clarence

6. anonymous

Yes, it's a definite integral, and I'm afraid I don't follow what triciaal has done... Sorry..

7. FibonacciChick666

so do integrals calculate area?

8. anonymous

Yes?

9. FibonacciChick666

yea. by definition they do

10. anonymous

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

so now, integrals calculate area under the curve. In this instance we need the area of a circle.

12. FibonacciChick666

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13. FibonacciChick666

and what jhanny elegantly put is the concept I am trying to illustrate

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

^@BAdhi is correct. This is an application of the previous

16. anonymous

So what do I actually have to do to solve this one? Just follow on from what I did previously?

17. FibonacciChick666

yep, see if it was applied correctly

18. anonymous

Okay then, I'll try that thanks

19. anonymous

After going through the same process that BAdhi did previously, it seems right to me

20. FibonacciChick666

I agree. Make sure you show your work with it on your paper :)

21. anonymous

I will, thanks! :)