Moderate -0.3 Part (i) is a straightforward application of Simpson's rule with given intervals requiring only careful arithmetic and function evaluation. Part (ii) is a routine exponential integration using simple substitution or recognition. Both parts are standard textbook exercises requiring no problem-solving insight, making this slightly easier than average for A-level.
4. (i) Use Simpson's rule with four intervals, each of width 0.25 , to estimate the value of the integral
$$\int _ { 0 } ^ { 1 } x \mathrm { e } ^ { 2 x } \mathrm {~d} x$$
(ii) Find the exact value of the integral
$$\int _ { \frac { 1 } { 2 } } ^ { 1 } e ^ { 1 - 2 x } d x$$
4. (i) Use Simpson's rule with four intervals, each of width 0.25 , to estimate the value of the integral
$$\int _ { 0 } ^ { 1 } x \mathrm { e } ^ { 2 x } \mathrm {~d} x$$
(ii) Find the exact value of the integral
$$\int _ { \frac { 1 } { 2 } } ^ { 1 } e ^ { 1 - 2 x } d x$$
\hfill \mbox{\textit{OCR C3 Q4 [7]}}