Standard +0.3 This is a straightforward integration problem requiring students to set up and evaluate a definite integral for area, then solve a simple equation. While it involves multiple steps (finding x-intercepts, setting up the integral, evaluating, and solving for a), each step uses standard AS-level techniques with no conceptual surprises. The 6 marks reflect the working required rather than genuine difficulty, making this slightly easier than average.
A curve has equation \(y = a^2 - x^2\), where \(a > 0\)
The area enclosed between the curve and the \(x\)-axis is 36 units.
Find the value of \(a\).
Fully justify your answer.
[6 marks]
A curve has equation $y = a^2 - x^2$, where $a > 0$
The area enclosed between the curve and the $x$-axis is 36 units.
Find the value of $a$.
Fully justify your answer.
[6 marks]
\hfill \mbox{\textit{AQA AS Paper 1 2022 Q7 [6]}}