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Question 595
a.

Determine ∫(10t4−6t3) dt\int \left( 10t^4 - \frac{6}{\sqrt[3]{t}} \right) \, dt ∫(10t4−3t​6​)dt.

[3]
b.

The rate of change of the mass, MMM grams, of a synthetic crystal with respect to time, ttt hours, is modeled by the differential equation

dMdt=10t4−6t3,t>0 \frac{dM}{dt} = 10t^4 - \frac{6}{\sqrt[3]{t}}, \quad t > 0 dtdM​=10t4−3t​6​,t>0

After 8 hours of growth, the mass of the crystal is measured to be 65520 grams.

Find an expression for MMM in terms of ttt.

[3]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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