Standard +0.8 This question requires setting up and evaluating two definite integrals with appropriate limits, involving both a chain rule integration (polynomial composition) and exponential integration. The 8-mark allocation and need to find exact values (requiring careful algebraic manipulation and likely fractional answers) elevates this above a routine integration question, though the techniques themselves are standard C3 content.
\includegraphics{figure_5}
The diagram shows the curves \(y = (1 - 2x)^5\) and \(y = e^{2x-1} - 1\). The curves meet at the point \((\frac{1}{2}, 0)\). Find the exact area of the region (shaded in the diagram) bounded by the \(y\)-axis and by part of each curve. [8]
\includegraphics{figure_5}
The diagram shows the curves $y = (1 - 2x)^5$ and $y = e^{2x-1} - 1$. The curves meet at the point $(\frac{1}{2}, 0)$. Find the exact area of the region (shaded in the diagram) bounded by the $y$-axis and by part of each curve. [8]
\hfill \mbox{\textit{OCR C3 Q5 [8]}}