Mathematical Methods — Question 9

QCAA 2022, Paper 1 · 1 mark

Q9 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 9

The approximate area under the curve

f(x)=\sqrt{2x+1}

between

x=0

and

x=4

using the trapezoidal rule with four strips is

(A)

2+\sqrt3+\sqrt5+\sqrt7

(B)

2+2(\sqrt3+\sqrt5+\sqrt7)

(C)

4+2(\sqrt3+\sqrt5+\sqrt7)

(D)

4+\sqrt3+\sqrt5+\sqrt7

ABCD

WORKED SOLUTION

1 mark

ANSWER

A —

2+\sqrt3+\sqrt5+\sqrt7

Worked solution

With four strips,

h=1

. The trapezoidal estimate is

\frac12[1+2(\sqrt3+\sqrt5+\sqrt7)+3]=2+\sqrt3+\sqrt5+\sqrt7

, so A.

Selects option A.

[1 mark]

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