Integration 2

1
Integration (2)

• Numerical methods
• Using the trapezium rule

2
Activity 1
Time allowed 2 minutes
Find the area of this shape.
4cm
3 cm
6 cm
3
Numerical methods

• Sometimes a function can be too tricky or
  impossible to integrate. In cases like this we
  can use a numerical method to get an approximate
  solution.
• One of the most common methods of doing this is
  using the Trapezium Rule.

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Trapezium Rule
If we wanted to find the area under the following
curve between 0.5 and 2.5, we could split it into
trapezia.
We have split this into four trapezia, so we
would say it has an interval of 4.
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Trapezium Rule
How can we find the values of a, b and h in the
case of the purple trapezium?
What is the area of the purple trapezium?
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Trapezium Rule
How can we find the values of a, b and h in the
case of the green trapezium?
What is the area of the green trapezium?
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Trapezium Rule
Find the area of the red and blue trapezia.
Use your answers to approximate the area under
the curve?
How could we have been more accurate?
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Generalising..
Area ½ h (end ordinates twice sum of
interior ordinates)
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Example
Using the Trapezium Rule with 6 ordinates,
calculate an approximation to
Is the answer an overestimate or an
underestimate??
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Activity
Time allowed rest of lesson
Turn to page 121 of your core 2 book and answer
questions in Exercise C.
Link