<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Sketch the curve \(y = x(x - 3)(x - 5)\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the following integrals.</span></div><ol class="i-list"><li><div class="list-item-paragraph">\(\displaystyle\int\nolimits_{0}^{3} x^3 - 9x^2 + 18x \, \mathrm{d}x\)</div></li><li><div class="list-item-paragraph">\(\displaystyle\int\nolimits_{3}^{6} x^3 - 9x^2 + 18x \, \mathrm{d}x\)</div></li><li><div class="list-item-paragraph">\(\displaystyle\int\nolimits_{0}^{6} x^3 - 9x^2 + 18x \, \mathrm{d}x\)</div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Explain why the area between the curve and the \(x\)-axis in the interval \(0 \le x \le 6\) is not the answer to <strong>(b)(iii)</strong>. And find the area between the curve and the \(x\)-axis for the interval \(0 \le x \le 6\).</span></div></li></ol>

Sketch the curve \(y = x(x - 3)(x - 5)\).

\[\displaystyle\int\nolimits_{0}^{3} x^3 - 9x^2 + 18x \, \mathrm{d}x\]

\[\displaystyle\int\nolimits_{3}^{6} x^3 - 9x^2 + 18x \, \mathrm{d}x\]

\[\displaystyle\int\nolimits_{0}^{6} x^3 - 9x^2 + 18x \, \mathrm{d}x\]

Explain why the area between the curve and the \(x\)-axis in the interval \(0 \le x \le 6\) is not the answer to **(b)(iii)**. And find the area between the curve and the \(x\)-axis for the interval \(0 \le x \le 6\).

Definite Integrals and Area under graph

Definite Integrals and Area under graph