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1.8 Integration

1.8 Integration

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Question 57

Four biologists are modeling the mass distribution m m\,m of a bacterial culture relative to the radial distance r r\,r from the center of a petri dish. They determine that the rate of change is given by dmdr=1r\displaystyle \frac{dm}{dr} = \frac{1}{r}drdm​=r1​ for r>0r > 0r>0. Each biologist proposes a different expression for the indefinite integral ∫1r dr\displaystyle \int \frac{1}{r} \, dr∫r1​dr:

Dr. Aris: m=ln⁡rm = \ln rm=lnr

Dr. Bond: m=Aln⁡rm = A \ln rm=Alnr

Dr. Chen: m=ln⁡(kr)m = \ln (kr)m=ln(kr)

Dr. Dyani: m=ln⁡r+cm = \ln r + cm=lnr+c

ai.

Explain the error in Dr. Aris's proposal.

[1]
aii.

Explain the error in Dr. Bond's proposal.

[1]
b.

Demonstrate why the expressions provided by Dr. Chen and Dr. Dyani are equivalent for certain values of the constants k k\,k and ccc.

[3]
Markscheme

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

160 exam-style questions on WJEC A Level Maths 1.8 Integration, covering 1.8.1 Integration, 1.8.2 Integration, and 1.8.3 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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