11.1 Integrating Standard Functions

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Four economists, Amara, Biruk, Chen, and Dalia, are attempting to determine the indefinite integral representing a total utility function:

$dv\int \frac{1}{v} \, dv$

for $v > 0$ . Each economist proposes a different general form for the result:

Amara: $dv=ln⁡v\int \frac{1}{v} \, dv = \ln v$

Biruk: $dv=Aln⁡v\int \frac{1}{v} \, dv = A \ln v$

Chen: $dv=ln⁡(kv)\int \frac{1}{v} \, dv = \ln(kv)$

Dalia: $dv=ln⁡v+C\int \frac{1}{v} \, dv = \ln v + C$

(i) Explain why Amara's result is incomplete.

(ii) Explain why Biruk's answer is incorrect as a general anti-derivative of $1v\frac{1}{v}$ .

[2]

Using the properties of logarithms, demonstrate why Chen and Dalia's forms can be considered equivalent for certain values of the constants $k$ and $C$ .

[2]

11.1 Integrating Standard Functions Questions

Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.