<p>It is given that $y = x^2\sqrt{2x-5}$, where $x \geq h$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{kx(x-2)}{\sqrt{2x-5}}$, where $k$ is an integer and determine the value of $h$ and of $k$.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Hence evaluate $\displaystyle\int\nolimits_{3}^{7} \left\{ \frac{10x(x-2)}{\sqrt{2x-5}} + 6 \right\} \mathrm{d}x$.<span class="inline-marks">[4]</span></div></li></ol>

It is given that $y = x^2\sqrt{2x-5}$, where $x \geq h$.

Show that $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{kx(x-2)}{\sqrt{2x-5}}$, where $k$ is an integer and determine the value of $h$ and of $k$.

Hence evaluate $\displaystyle \displaystyle\int\nolimits_{3}^{7} \left\{ \frac{10x(x-2)}{\sqrt{2x-5}} + 6 \right\} dx$.

Hence evaluate $\displaystyle \displaystyle\int\nolimits_{3}^{7} \left\{ \frac{10x(x-2)}{\sqrt{2x-5}} + 6 \right\} \mathrm{d}x$.

Integration Techniques - Integration Techniques - General

Integration Techniques - Integration Techniques - General