Further integration — Question 179

Original QCE Vault practice · 4 marks

Q179 · Practice questionTechnology-freeComplex familiar4 marks

QUESTION 179 (4 marks)

The graphs of

y=2x

and

y=x^2

are shown. Determine the area of the bounded region between the curves.

WORKED SOLUTION

4 marks

ANSWER

\dfrac43

square units.

Worked solution

The curves meet when

x^2=2x

, so

x=0,2

. On this interval

2x\ge x^2

, hence the area is

\int_0^2(2x-x^2)\,dx=[x^2-x^3/3]_0^2=4/3

Finds the intersection values.

[1 mark]

Sets up the correct area integral.

[1 mark]

Finds an antiderivative.

[1 mark]

Evaluates the area.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.

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