Further integration — Question 128

Original QCE Vault practice · 3 marks

Q128 · Practice questionTechnology-freeSimple familiar3 marks

QUESTION 128 (3 marks)

Determine the area enclosed by the curve

y=x(4-x)

and the

x

-axis.

WORKED SOLUTION

3 marks

ANSWER

\dfrac{32}{3}

square units.

Worked solution

The curve meets the axis at

x=0

and

x=4

. The area is

\int_0^4(4x-x^2)dx=[2x^2-x^3/3]_0^4=32/3

Identifies the correct limits.

[1 mark]

Forms and evaluates the definite integral.

[1 mark]

Obtains

32/3

square units.

[1 mark]

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

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