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4 marksIntegration

CAPE Integrated Mathematics · 2017 · Paper 2 · Question 6(a)

Determine \int \cos(5x - 3) \, dx.

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  1. 6(b)Show that \int_{1}^{3} (x^{\frac{5}{2}} - 2) \, dx is approximately 9.08.[5 marks]
  2. 6(c)(i)A radioactive substance decays at a rate of \frac{dR}{dt} = -kR, where t is time and k is a constant. Show that R satisfies the equation R(t) = e^{-kt + c}.[5 marks]
  3. 6(c)(ii)If at time t = 0 the substance has an original mass of 500 mg, show that R(t) = 500e^{-kt}.[4 marks]
  4. 6(d)Find the area bounded by the function f(x) = \frac{4}{3}x^3 - 7.5x^2 + 10x, the x-axis and the line x = C, where C is the critical value of f(x) which…[7 marks]

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