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1.11 H: Integration

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Question 183

The temperature HHH (in ∘C^{\circ}\text{C}∘C) of a specialized thermal probe is modeled as a function of time ttt (in seconds, t>0t > 0t>0), where H=g(t)H = g(t)H=g(t).

It is known that:

  • At t=9t = 9t=9, the temperature of the probe is 15∘C15^{\circ}\text{C}15∘C.
  • The rate of change of temperature is given by g′(t)=45t2+32t−2g'(t) = \dfrac{45}{t^2} + \dfrac{3}{2\sqrt{t}} - 2g′(t)=t245​+2t​3​−2
a.

Determine the equation of the tangent to the curve H=g(t)H = g(t)H=g(t) at the point where t=9t = 9t=9. Give your answer in the form H=mt+cH = mt + cH=mt+c, where m m\,m and c c\,c are constants.

[4]
b.

Find an expression for g(t)g(t)g(t) in its simplest form.

[6]
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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