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1.11 H: Integration

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Question 127
a.

Find ∫(12x2−5xx) dx\int \left( 12x^2 - \dfrac{5}{x\sqrt{x}} \right) \, dx ∫(12x2−xx​5​)dx

[3]
b.

The rate of change of the mass, MMM grams, of a chemical precipitate over time ttt minutes is modelled by the differential equation

dMdt=12t2−5tt,t>0 \dfrac{dM}{dt} = 12t^2 - \dfrac{5}{t\sqrt{t}}, \quad t > 0 dtdM​=12t2−tt​5​,t>0

Given that at t=4t = 4t=4, the mass of the precipitate is 265 grams, determine an expression for MMM in terms of ttt.

[3]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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