<ol class="abc-list"><li data-list-item-id="item-3a"><div class="list-item-paragraph">A curve has the equation \(y = x^3 \ln 4x\), where&nbsp;\(x &gt; 0\).<br>Find an expression for&nbsp;\(\frac{\mathrm{d}y}{\mathrm{d}x}\).<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-3b"><div class="list-item-paragraph">Hence, find \(\int_{1}^{3} x^2 \ln 4x \; \mathrm{d}x\).<span class="inline-marks">[4]</span></div></li></ol>

A curve has the equation \(y = x^3 \ln 4x\), where \(x > 0\).
Find an expression for \(\frac{\mathrm{d}y}{\mathrm{d}x}\).

Hence, find \(\int_{1}^{3} x^2 \ln 4x \; \mathrm{d}x\).

Applications of Integration

Applications of Integration