Additional Mathematics 0606 / Calculus — Integration / 2.672.67: Secant derivative and logarithmic integration0606/23/M/J/20 — Question 12 · 11 marksMark as done · Save for later · Show all solutions(a)(i)Given that f(x)=1cosxf(x) = \dfrac{1}{\cos x}f(x)=cosx1, show that f′(x)=tanxsecxf'(x) = \tan x \sec xf′(x)=tanxsecx.[3]▸ Answer(a)(ii)Hence find ∫(3tanxsecx−e3x4)dx\displaystyle\int \left(3\tan x \sec x - \sqrt[4]{\mathrm{e}^{3x}}\right)\mathrm{d}x∫(3tanxsecx−4e3x)dx.[3]▸ Answer(b)Given that ∫25ppx+10 dx=ln2\displaystyle\int_{2}^{5} \frac{p}{px + 10}\,\mathrm{d}x = \ln 2∫25px+10pdx=ln2, find the value of the positive constant ppp.[5]▸ Answer▸ Official mark scheme← 2.46: Definite integrals of rational and exponential functions1.22: Area between a cosine curve and a horizontal line →
