Moderate -0.8 This is a straightforward application of the trapezium rule with clear parameters (three intervals, defined limits). The only work required is calculating function values at four points and applying the standard formula. While ln(1 + sin x) requires careful calculator work, there's no conceptual challenge or problem-solving—just mechanical execution of a standard numerical method.
1 Use the trapezium rule with three intervals to estimate the value of
$$\int _ { 0 } ^ { \frac { 1 } { 2 } \pi } \ln ( 1 + \sin x ) \mathrm { d } x$$
giving your answer correct to 2 decimal places.
State or imply ordinates \(0, 0.405465..., 0.623810..., 0.693147...\)
B1
Use correct formula, or equivalent, with \(h = \frac{1}{6}\pi\) and four ordinates
M1
Obtain answer 0.72
A1
[3]
State or imply ordinates $0, 0.405465..., 0.623810..., 0.693147...$ | B1 |
Use correct formula, or equivalent, with $h = \frac{1}{6}\pi$ and four ordinates | M1 |
Obtain answer 0.72 | A1 | [3]
1 Use the trapezium rule with three intervals to estimate the value of
$$\int _ { 0 } ^ { \frac { 1 } { 2 } \pi } \ln ( 1 + \sin x ) \mathrm { d } x$$
giving your answer correct to 2 decimal places.
\hfill \mbox{\textit{CAIE P3 2015 Q1 [3]}}