Mathematical Methods — Question 4

QCAA 2021, Paper 2 · 1 mark

Q4 · 2021 · Technology-activeSimple familiar1 mark

QUESTION 4

Using the trapezoidal rule with an interval size of 1, the approximate value of the integral

\int_0^3 0.5^x\,dx

(A)

1.25

(B)

1.26

(C)

1.31

(D)

1.88

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

Using

h=1

and values

1,0.5,0.25,0.125

, the trapezoidal estimate is

\frac12[1+2(0.5)+2(0.25)+0.125]=1.3125\approx1.31

Selects option C.

[1 mark]

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