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Question 525
i.

The rate of increase of a substance's temperature, T T\,T in degrees Celsius, over time t t\,t minutes is modeled by the equation

dTdt=52t+3,t≥0 \frac{dT}{dt} = \frac{5}{2t + 3}, \quad t \ge 0 dtdT​=2t+35​,t≥0

Calculate the exact change in temperature between t=1t = 1t=1 and t=6t = 6t=6 minutes, giving your answer in its simplest form.

[3]
ii.

g(x)=2x3−11x2−8x+87(x−4)2g(x) = \dfrac{2x^3 - 11x^2 - 8x + 87}{(x - 4)^2}g(x)=(x−4)22x3−11x2−8x+87​ for x>4x > 4x>4.

Given that g(x)=Ax+B+C(x−4)2g(x) = Ax + B + \dfrac{C}{(x - 4)^2}g(x)=Ax+B+(x−4)2C​ where AAA, B B\,B and C C\,C are constants to be determined, find

∫g(x) dx \int g(x) \, dx ∫g(x)dx
[5]
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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