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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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? :/

Mathematics
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So, what does an integral do?
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|dw:1444023306505:dw|
I assume your integral in the question is not indefinite? @Clarence
Yes, it's a definite integral, and I'm afraid I don't follow what triciaal has done... Sorry..
so do integrals calculate area?
Yes?
yea. by definition they do
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.
so now, integrals calculate area under the curve. In this instance we need the area of a circle.
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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 \(g(t) = \ln(t+2)\)
^@BAdhi is correct. This is an application of the previous
So what do I actually have to do to solve this one? Just follow on from what I did previously?
yep, see if it was applied correctly
Okay then, I'll try that thanks
After going through the same process that BAdhi did previously, it seems right to me
I agree. Make sure you show your work with it on your paper :)
I will, thanks! :)

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