Further integration — Question 41

Original QCE Vault practice · 3 marks

Q41 · Practice questionTechnology-freeComplex familiar3 marks

QUESTION 41 (3 marks)

For

0\le x\le1

, the graph

y=kx(1-x)

lies above the

x

-axis. The area between the graph and the

x

-axis is 2 square units. Determine

k

WORKED SOLUTION

3 marks

ANSWER

k=12

Worked solution

\int_0^1kx(1-x)dx=k[x^2/2-x^3/3]_0^1=k/6

. Setting

k/6=2

gives

k=12

Sets up the area integral.

[1 mark]

Evaluates the integral as

k/6

[1 mark]

Determines

k=12

[1 mark]

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

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