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IB Maths AI SL 5.5 Integration as Anti-Differentiation

IB Maths AI SL 5.5 Integration as Anti-Differentiation
IB Mathematics: applications and interpretation guide, first assessment 2021

Practise recovering functions from rates of change and using definite integrals for areas, distances and accumulated quantities.

How this is tested

  • integrate a rate function and use an initial condition to determine the constant
  • split motion at velocity sign changes before adding the total distance travelled
  • evaluate definite integrals for signed area or accumulated quantities in context

Question 2(c)

[Maximum number: 5]

The height of a plant, h cmh \mathrm{~cm}, depends on the time, t days, after it is planted.
For the first 15 days, the rate of change of the height of the plant is modelled as

dh dt=1.2−0.1t, where 0≤t≤15.\frac{\mathrm{d} h}{\mathrm{~d} t}=1.2-0.1 t, \text { where } 0 \leq t \leq 15 .

Find an expression for h in terms of t, for 0≤t≤150 \leq t \leq 15.