Q290 · Practice questionTechnology-freeComplex familiar5 marks
QUESTION 290 (5 marks)
The graph of is shown for .
a)[2 marks]
Evaluate .
b)[3 marks]
Determine the total area enclosed between this graph and the -axis on the stated interval.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
a) . b) square units.
Worked solution
a) .
b) The curve is below the axis on and above elsewhere. The central area is ; each outer area is . Total area is .
Exact answers unless rounding is specified; equivalent forms accepted.
a) Determines an antiderivative.
a) Evaluates the signed integral.
b) Splits at x = -1 and 1 with correct signs.
b) Evaluates the region areas.
b) Gives the total area.
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