<p>It is given that $I=\displaystyle\int{\frac{x}{\sqrt{4-2x}}\,\mathrm{d}x}$.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Use integration by parts to find an expression for $I$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Use the substitution $u=4-2x$ to find another expression for $I$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Show algebraically that the answers to parts (a) and (b) differ by a constant.</span></div><p style="text-align: right;">[2]</p></li></ol>

It is given that $I=\displaystyle\displaystyle \displaystyle\int{\frac{x}{\sqrt{4-2x}}\,\mathrm{d}x}$.

Use integration by parts to find an expression for $I$.

Use the substitution $u=4-2x$ to find another expression for $I$.

Show algebraically that the answers to parts (a) and (b) differ by a constant.

Integration by Substitution

Techniques of Integration

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

2022 YIJC P2 Q1

2022 YIJC P2 Q1

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