Additional Mathematics 0606 / Trigonometry / 3.223.22: Integrals with sine and identity0606/23/M/J/21 — Question 8 · 8 marksMark as done · Save for later · Show all solutions(a)(i)Find ∫sin(ϕ+π3) dϕ\displaystyle\int \mathrm{sin}\left(\dfrac{\phi + \pi}{3}\right)\,\mathrm{d}\phi∫sin(3ϕ+π)dϕ.[2]▸ Answer(a)(ii)Find ∫(5 sin2θ+5 cos2θ) dθ\displaystyle\int\bigl(5\,\mathrm{sin}^{2}\theta + 5\,\mathrm{cos}^{2}\theta\bigr)\,\mathrm{d}\theta∫(5sin2θ+5cos2θ)dθ.[2]▸ Answer(b)Show that ∫1e(2x+1x2)dx=3e−1e\displaystyle\int_{1}^{\mathrm{e}}\left(\frac{2}{x} + \frac{1}{x^{2}}\right)\mathrm{d}x = \frac{3\mathrm{e} - 1}{\mathrm{e}}∫1e(x2+x21)dx=e3e−1.[4]▸ Answer▸ Official mark scheme← 3.21: Ln curve sketch and tangent3.1: Trapezium with surds: perimeter, area, tan and sec →
