| Exam Board | OCR |
|---|
| Module | C4 (Core Mathematics 4) |
|---|
| Topic | Integration by Parts |
|---|
8. (i) Find
$$\int x ^ { 2 } \mathrm { e } ^ { \frac { 1 } { 2 } x } \mathrm {~d} x$$
(ii) Using the substitution \(u = \sin t\), evaluate
$$\int _ { 0 } ^ { \frac { \pi } { 2 } } \sin ^ { 2 } 2 t \cos t \mathrm {~d} t$$