Mathematical Methods — Question 8

QCAA 2024, Paper 2 · 1 mark

Q8 · 2024 · Technology-activeSimple familiar1 mark

QUESTION 8

Calculate the total enclosed area between the graph of

y=x^2-x-6

and the

x

-axis from

x=1

x=5

(A)

5.33

(B)

7.33

(C)

12.67

(D)

20.00

ABCD

WORKED SOLUTION

1 mark

ANSWER

D — 20.00

Worked solution

The curve crosses the

x

-axis at

x=3

. Thus the total area is

-\int_1^3(x^2-x-6)\,dx+\int_3^5(x^2-x-6)\,dx=7.33\ldots+12.66\ldots=20.00

, so option D.

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.