June 2023 Paper 1 Q3
3 Find \(\displaystyle\int \left(2x^4 - x\sqrt{x}\right)\mathrm{d}x\). [3]
| Scheme | Marks | AO |
|---|---|---|
| \(\displaystyle\int \left(2x^4 - x\sqrt{x}\right)\mathrm{d}x = \int \left(2x^4 - x^{\frac{3}{2}}\right)\mathrm{d}x\) | M1 | 3.1a |
| \(\dfrac{2x^5}{5} - \dfrac{x^{5/2}}{5/2}\ [+c]\) | M1 | 1.1b |
| \(\dfrac{2x^5}{5} - \dfrac{2x^{\frac{5}{2}}}{5} + c\) | A1 | 1.1b |
| [3] |
Notes
M1: Expresses integrand in index form soi
M1: Integrates at least one term
A1: Any form. Arbitrary constant must be seen.
Correct answer for the second term by a different method implies the first M1