OCR C2 — Question 3 7 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeFind curve from gradient
DifficultyModerate -0.3 This is a straightforward integration question requiring students to integrate a simple expression, apply an initial condition to find the constant, then substitute x=4. The integration is routine (power rule only), and the algebraic manipulation is minimal. Slightly easier than average due to its mechanical nature, though the fractional powers require care.
Spec1.08b Integrate x^n: where n != -1 and sums

Given that $$\frac{dy}{dx} = 3\sqrt{x} - x^2,$$ and that \(y = \frac{4}{3}\) when \(x = 1\), find the value of \(y\) when \(x = 4\). [7]

Given that
$$\frac{dy}{dx} = 3\sqrt{x} - x^2,$$

and that $y = \frac{4}{3}$ when $x = 1$, find the value of $y$ when $x = 4$. [7]

\hfill \mbox{\textit{OCR C2  Q3 [7]}}