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1.8 Integration

1.8 Integration

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Question 249

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

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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