Area under curve using integration

Questions requiring calculation of the area of a region bounded by a curve, axes, and/or lines, using definite integration after applying the chain rule to find antiderivatives.

1 questions · Moderate -0.3

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CAIE P1 2021 March Q11
12 marks Moderate -0.3
11
\includegraphics[max width=\textwidth, alt={}, center]{54f3f051-e124-470d-87b5-8e25c35248a9-18_497_1049_264_548} The diagram shows the curve with equation \(y = 9 \left( x ^ { - \frac { 1 } { 2 } } - 4 x ^ { - \frac { 3 } { 2 } } \right)\). The curve crosses the \(x\)-axis at the point \(A\).
  1. Find the \(x\)-coordinate of \(A\).
  2. Find the equation of the tangent to the curve at \(A\).
  3. Find the \(x\)-coordinate of the maximum point of the curve.
  4. Find the area of the region bounded by the curve, the \(x\)-axis and the line \(x = 9\).
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