Additional Mathematics 0606 / Calculus — Integration / 1.181.18: Chain rule and integration by recognition0606/11/O/N/18 — Question 8 · 8 marksMark as done · Save for later · Show all solutions(i)Find ddx(5x2+4)32\dfrac{\mathrm{d}}{\mathrm{d}x}(5x^{2} + 4)^{\frac{3}{2}}dxd(5x2+4)23.[2]▸ Answer(ii)Hence find ∫x(5x2+4)12 dx\displaystyle\int x(5x^{2} + 4)^{\frac{1}{2}}\,\mathrm{d}x∫x(5x2+4)21dx.[2]▸ Answer(iii)Given that ∫0ax(5x2+4)12 dx=1915\displaystyle\int_{0}^{a} x(5x^{2} + 4)^{\frac{1}{2}}\,\mathrm{d}x = \dfrac{19}{15}∫0ax(5x2+4)21dx=1519, find the value of the positive constant aaa.[4]▸ Answer▸ Official mark scheme← 2.63: Area between a parabola and a horizontal line1.49: Finding a curve from second derivative →
