<ol class="abc-list"><li data-list-item-id="imported-item-block-0-item-0" data-list-item-path="imported-item-block-0-item-0"><div class="list-item-paragraph">Solve exactly the inequality \(\mathrm{e}^{x} \geqslant 2\mathrm{e}^{-x} + 1\).<span class="inline-marks">[3]</span></div></li><li data-list-item-id="imported-item-block-0-item-1" data-list-item-path="imported-item-block-0-item-1"><div class="list-item-paragraph">Hence find \(\int_{0}^{1} \left\vert{} \mathrm{e}^{x} - 2\mathrm{e}^{-x} - 1 \right\vert{} \mathrm{d}x\), giving your answer in exact form.<span class="inline-marks">[4]</span></div></li></ol>

Solve exactly the inequality \(\mathrm{e}^{x} \geqslant 2\mathrm{e}^{-x} + 1\).

Hence find \(\int_{0}^{1} \left\vert{} \mathrm{e}^{x} - 2\mathrm{e}^{-x} - 1 \right\vert{} \mathrm{d}x\), giving your answer in exact form.

Integrals involving Modulus Functions

Applications of Integration

International Baccalaureate Mathematics: Analysis and Approaches Higher Level