OCR C2 2009 January — Question 4 7 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2009
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAreas Between Curves
TypeCurve with Horizontal Line
DifficultyModerate -0.5 This is a straightforward area-between-curves question requiring students to set up and evaluate ∫₋₂² (19 - (x⁴ + 3))dx. The symmetry simplifies the calculation, and integrating x⁴ is basic C2 content. It's slightly easier than average because the intersection points are given, the integrand is simple, and no problem-solving is needed—just direct application of the standard method.
Spec1.08e Area between curve and x-axis: using definite integrals

4 \includegraphics[max width=\textwidth, alt={}, center]{bbee5a50-4a32-4171-8713-8eb38914a511-3_570_853_269_644} The diagram shows the curve \(y = x ^ { 4 } + 3\) and the line \(y = 19\) which intersect at \(( - 2,19 )\) and \(( 2,19 )\). Use integration to find the exact area of the shaded region enclosed by the curve and the line.

4\\
\includegraphics[max width=\textwidth, alt={}, center]{bbee5a50-4a32-4171-8713-8eb38914a511-3_570_853_269_644}

The diagram shows the curve $y = x ^ { 4 } + 3$ and the line $y = 19$ which intersect at $( - 2,19 )$ and $( 2,19 )$. Use integration to find the exact area of the shaded region enclosed by the curve and the line.

\hfill \mbox{\textit{OCR C2 2009 Q4 [7]}}