Standard +0.3 This is a straightforward partial fractions integration problem with clear numerical limits and a specific target answer to verify. It requires decomposing the fraction, integrating logarithmic terms, and evaluating at boundaries—all standard techniques for this topic. The verification aspect (showing it equals ln 50) makes it slightly easier than open-ended questions, as students can check their work. This is slightly above routine drill but well within typical A-level expectations.
State or imply form \(\frac{A}{2x+1} + \frac{B}{x+2}\)
B1
Use relevant method to find \(A\) or \(B\)
M1
Obtain \(\frac{4}{2x+1} - \frac{1}{x+2}\)
A1
Integrate and obtain \(2\ln(2x+1) - \ln(x+2)\) (ft on their \(A, B\))
B1
B1
Apply limits to integral containing terms \(a\ln(2x+1)\) and \(b\ln(x+2)\) and apply a law of logarithms correctly.
M1
Obtain given answer in 50 correctly
A1
[7]
State or imply form $\frac{A}{2x+1} + \frac{B}{x+2}$ | B1 |
Use relevant method to find $A$ or $B$ | M1 |
Obtain $\frac{4}{2x+1} - \frac{1}{x+2}$ | A1 |
Integrate and obtain $2\ln(2x+1) - \ln(x+2)$ (ft on their $A, B$) | B1 | B1 |
Apply limits to integral containing terms $a\ln(2x+1)$ and $b\ln(x+2)$ and apply a law of logarithms correctly. | M1 |
Obtain given answer in 50 correctly | A1 | [7]