Easy -1.2 This is a straightforward integration of polynomial terms requiring only basic power rule application. Students need to rewrite √x as x^(1/2), combine powers, then integrate using the standard formula x^n → x^(n+1)/(n+1). No problem-solving or conceptual insight required—purely routine manipulation below average difficulty.
Any form. Arbitrary constant must be seen. Correct answer for the second term by a different method implies the first M1
Total: [3]
## Question 3:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\int(2x^4 - x\sqrt{x})\,dx = \int\left(2x^4 - x^{\frac{3}{2}}\right)dx$ | M1 | Expresses integrand in index form |
| $\frac{2x^5}{5} - \frac{x^{5/2}}{5/2} \left[+c\right]$ | M1 | Integrates at least one term |
| $\frac{2x^5}{5} - \frac{2x^{\frac{5}{2}}}{5} + c$ | A1 | Any form. Arbitrary constant must be seen. Correct answer for the second term by a different method implies the first M1 |
**Total: [3]**