| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | January |
| Marks | 3 |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Find indefinite integral of polynomial/power |
| Difficulty | Easy -1.2 This is a straightforward application of standard power rule integration requiring students to rewrite terms in index form (√x = x^(1/2), 1/x² = x^(-2)) and apply the formula ∫x^n dx = x^(n+1)/(n+1) + C. It's routine manipulation with no problem-solving or conceptual challenge, making it easier than average but not trivial since it requires correct handling of fractional and negative indices. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums |
1.
$$f ( x ) = 6 x + 9 \sqrt { x } - \frac { 4 } { x ^ { 2 } } , x > 0 .$$
Find a fully simplified expression for
$$\int f ( x ) d x$$
\hfill \mbox{\textit{SPS SPS SM 2021 Q1 [3]}}