Further integration — Question 91

Original QCE Vault practice · 4 marks

Q91 · Practice questionTechnology-freeComplex familiar4 marks

QUESTION 91 (4 marks)

Determine the area enclosed by the curves

y=4-x^2

and

y=x+2

WORKED SOLUTION

4 marks

ANSWER

\dfrac92

square units.

Worked solution

The curves intersect when

x^2+x-2=0

, so

x=-2,1

. The area is

\int_{-2}^{1}(2-x-x^2)dx=9/2

Finds the intersections

x=-2,1

[1 mark]

Sets up the correct area integral.

[1 mark]

Finds a correct antiderivative.

[1 mark]

Obtains

9/2

square units.

[1 mark]

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

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