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\includegraphics[max width=\textwidth, alt={}, center]{cf77e51a-1d3f-423a-be59-96ec60fbeb67-2_568_959_269_593} The diagram shows the curve with equation \(y = \ln ( \cos x )\), for \(0 \leqslant x \leqslant 1.5\). The region bounded by the curve, the \(x\)-axis and the line \(x = 1.5\) has area \(A\). The region is divided into five strips, each of width 0.3 .

1. By considering the set of rectangles indicated in the diagram, find an upper bound for \(A\). Give the answer correct to 3 decimal places.
2. By considering another set of five suitable rectangles, find a lower bound for \(A\). Give the answer correct to 3 decimal places.
3. How could you reduce the difference between the upper and lower bounds for \(A\) ?