Additional Mathematics 0606 / Straight-line graphs / 3.753.75: Differentiate y=x3lnxy=x^{3}\ln xy=x3lnx; definite integral0606/13/O/N/24 — Question 7 · 6 marksMark as done · Save for later · Show all solutions(a)Given y=x3lnxy=x^{3}\ln xy=x3lnx, find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}dxdy.[2]▸ Answer(b)Hence find ∫12x2lnx dx\displaystyle\int_{1}^{2} x^{2}\ln x\,\mathrm{d}x∫12x2lnxdx in the form lna+b\ln a+blna+b.[4]▸ Answer▸ Official mark scheme← 3.74: Linear law: lny\ln ylny against x2x^{2}x2 for y=Abx2y=Ab^{x^{2}}y=Abx23.76: Line meets curve; perpendicular bisector →
