Moderate -0.8 This is a straightforward application of the standard integral ∫(1/x)dx = ln|x| + c with a linear substitution. Students need only recognize the form, integrate to get ln|x+2|, apply limits 0 and 6, and simplify ln(8) - ln(2) = ln(4) = 2ln(2). It's a routine textbook exercise testing basic logarithmic integration with minimal algebraic manipulation, making it easier than average.
Use law for the logarithm of a product, quotient or a power
M1
Obtain given answer following full and correct working
A1
[4]
Obtain integral $\ln(x + 2)$ | B1 |
Substitute correct limits correctly | M1 |
Use law for the logarithm of a product, quotient or a power | M1 |
Obtain given answer following full and correct working | A1 | [4]