Additional Mathematics 0606 / Calculus — Integration / 2.382.38: Integration of power, sine and exponential functions0606/22/M/J/18 — Question 11 · 11 marksMark as done · Save for later · Show all solutions(a)Find ∫2x−13 dx\displaystyle\int \sqrt[3]{2x - 1}\,\mathrm{d}x∫32x−1dx.[2]▸ Answer(b)(i)Find ∫sin4x dx\displaystyle\int \sin 4x\,\mathrm{d}x∫sin4xdx.[2]▸ Answer(b)(ii)Hence evaluate ∫π/8π/4sin4x dx\displaystyle\int_{\pi/8}^{\pi/4} \sin 4x\,\mathrm{d}x∫π/8π/4sin4xdx.[2]▸ Answer(c)Show that ∫0ln8ex/3 dx=3\displaystyle\int_{0}^{\ln 8} \mathrm{e}^{x/3}\,\mathrm{d}x = 3∫0ln8ex/3dx=3.[5]▸ Answer▸ Official mark scheme← 2.37: Differentiating and integrating with square roots of sine1.15: Area between an exponential curve and a chord →
