Mathematical Methods — Question 1

QCAA 2020, Paper 1 · 1 mark

Q1 · 2020 · Technology-freeSimple familiar1 mark

QUESTION 1

The graphs of

f(x)=e^x

and

g(x)=x^2-1

are shown. The area of the shaded section bounded by these graphs between the lines

x=0

and

x=1

(A)

1-e

(B)

e-2

(C)

e-\frac{5}{3}

(D)

e-\frac{1}{3}

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

The required area is

\int_0^1[e^x-(x^2-1)]\,dx=[e^x-\frac{x^3}{3}+x]_0^1=e-\frac13

, so option D is correct.

Selects option D.

[1 mark]

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