Further integration — Question 46

Original QCE Vault practice · 4 marks

Q46 · Practice questionTechnology-freeComplex unfamiliar4 marks

QUESTION 46 (4 marks)

The curves

y=x^2

and

y=kx

, where

k>0

, enclose a bounded region of area

\dfrac92

. Determine

k

WORKED SOLUTION

4 marks

ANSWER

k=3

Worked solution

The curves intersect at

x=0

and

x=k

. The area is

\int_0^k(kx-x^2)dx=k^3/6

. Set

k^3/6=9/2

to obtain

k^3=27

, so

k=3

Determines intersections

x=0,k

[1 mark]

Sets up the area integral.

[1 mark]

Simplifies the area to

k^3/6

[1 mark]

Solves to obtain

k=3

[1 mark]

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

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