Additional Mathematics 0606 / Calculus — Integration / 1.511.51: Differentiation and integration with fractional powers0606/12/O/N/18 — Question 6 · 6 marksMark as done · Save for later · Show all solutions(i)Find ddx(5x2−125)23\dfrac{\mathrm{d}}{\mathrm{d}x}(5x^{2} - 125)^{\frac{2}{3}}dxd(5x2−125)32.[2]▸ Answer(ii)Using your answer to part (i), find ∫x(5x2−125)−13 dx\displaystyle\int x(5x^{2} - 125)^{-\frac{1}{3}}\,\mathrm{d}x∫x(5x2−125)−31dx.[2]▸ Answer(iii)Hence find ∫610x(5x2−125)−13 dx\displaystyle\int_{6}^{10} x(5x^{2} - 125)^{-\frac{1}{3}}\,\mathrm{d}x∫610x(5x2−125)−31dx.[2]▸ Answer▸ Official mark scheme← 1.49: Finding a curve from second derivative1.80: Area between a parabola and a line →
