3.7.5 Integration (A-level only)

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Question 14

The rate of biomass accumulation in a soil sample, $B$ (measured in mg per day), is modeled as a function of the nitrogen concentration $n$ (in parts per million) by the equation:

\frac{5n - 3}{n^2 - n}, \quad n > 1

a.

Express $B (n)$ in partial fractions.

[3]

b.

Hence find $dn\displaystyle \int B(n) \, dn$ .

[3]

c.

Use your answer to part (b) to find the value of $k$ for which the total biomass accumulation between concentration levels $n = k$ and $n = 2 k$ is exactly $ln⁡72\ln 72$ , where $k > 1$ .

\int_k^{2k} B(n) \, dn = \ln 72

[4]

3.7.5 Integration (A-level only)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Question 14

The rate of biomass accumulation in a soil sample, $B$ (measured in mg per day), is modeled as a function of the nitrogen concentration $n$ (in parts per million) by the equation:

\frac{5n - 3}{n^2 - n}, \quad n > 1

a.

Express $B (n)$ in partial fractions.

[3]

b.

Hence find $dn\displaystyle \int B(n) \, dn$ .

[3]

c.

Use your answer to part (b) to find the value of $k$ for which the total biomass accumulation between concentration levels $n = k$ and $n = 2 k$ is exactly $ln⁡72\ln 72$ , where $k > 1$ .

\int_k^{2k} B(n) \, dn = \ln 72

[4]

3.7.5 Integration (A-level only)

Question 14

3.7.5 Integration (A-level only) Questions

3.7.5 Integration (A-level only)

Question 14

3.7.5 Integration (A-level only) Questions