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]

1.8.2 Integrating x^n Questions

A Level
Maths
1.8.2 Integrating x^n

A Level
Maths OCR
Question bank

1.8.2 Integrating x^n

Easy Medium

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

Question 62

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

\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]

1.8.2 Integrating x^n Questions

A Level
Maths
1.8.2 Integrating x^n