Integration - Area Bounded by a Curve and Straight Lines
Integration - Area Bounded by a Curve and Straight Lines
The diagram shows part of the curve \(y=4-\mathrm{e}^{\frac{1}{2}x}\) which cuts the axes at \(A\) and at \(B\).
- Find the coordinates of \(A\) and of \(B\).
The tangent to the curve at \(A\) meets the \(x\)-axis at \(C\).
- Find the coordinates of \(C\).
- Find the area of the shaded region.
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Answer:(a) \(A=(0,3),\ B=(4\ln2,0)\) (b) \(C=(6,0)\) (c) \((15-16\ln2)\text{ units}^2\)
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