11.1 Integrating Standard Functions
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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]

11.1 Integrating Standard Functions Questions

Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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11.1 Integrating Standard Functions Questions

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