Additional Mathematics 0606 / Calculus — Integration / 2.492.49: Differentiating and integrating lnx\ln xlnx0606/22/O/N/17 — Question 9 · 8 marksMark as done · Save for later · Show all solutions(i)Find ddx(xlnx)\dfrac{\mathrm{d}}{\mathrm{d}x}(x\ln x)dxd(xlnx).[2]▸ Answer(ii)Hence find ∫lnx dx\displaystyle\int \ln x\,\mathrm{d}x∫lnxdx.[2]▸ Answer(iii)Hence, given that k>0k > 0k>0, show that ∫k2klnx dx=k(ln4k−1)\displaystyle\int_{k}^{2k} \ln x\,\mathrm{d}x = k(\ln 4k - 1)∫k2klnxdx=k(ln4k−1).[4]▸ Answer▸ Official mark scheme← 2.48: Curve from normal gradient and tangent equation2.51: Tangent to a quadratic and shaded area →
