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3.7 Integration (A-level only)

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Question 89
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

3.7 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7 Integration (A-level only)

221 exam-style questions on WJEC A Level Maths 3.7 Integration (A-level only), covering 3.7.1 Integration (A-level only), 3.7.2 Integration (A-level only), 3.7.3 Integration (A-level only), 3.7.4 Integration (A-level only), 3.7.5 Integration (A-level only), and 3.7.6 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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