Dark mode

Mathematical Methods — Question 9

QCAA 2025, Paper 1 · 1 mark

Q9 · 2025 · Technology-freeSimple familiar1 mark

QUESTION 9

Determine

\displaystyle\int\frac{1}{7x-4}\,dx

, where

x>\frac47

.

(A)

\frac17\ln(7x-4)+c

(B)

\frac47\ln(7x-4)+c

(C)

7\ln(7x-4)+c

(D)

\ln(7x-4)+c

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

A —

\frac17\ln(7x-4)+c

Worked solution

Let

u=7x-4

, so

du=7\,dx

. Then

\int\frac{1}{7x-4}\,dx=\frac17\ln(7x-4)+c,

so option A.

Selects option A.

[1 mark]

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

View the full QCAA marking guide

Related questions

Q1 · 2025 QCAA · Paper 1 · 1 mark
Determine the value of $\displaystyle\int_1^2 3x^2\,dx$ .
Question and worked solution
Q2 · 2025 QCAA · Paper 1 · 1 mark
State the domain of the function $y=\ln(x)$ .
Question and worked solution
Q3 · 2025 QCAA · Paper 1 · 1 mark
A council wants to survey residents about a new dog park. Which sampling method would best minimise bias in the survey?
Question and worked solution
Q4 · 2025 QCAA · Paper 1 · 1 mark
Solve for $x$ in the equation $\ln(x)+\ln(2)=\ln(8)$ .
Question and worked solution