Dark mode

Mathematical Methods — Question 5

QCAA 2024, Paper 1 · 1 mark

Q5 · 2024 · Technology-freeSimple familiar1 mark

QUESTION 5

Determine

\displaystyle\int_a^b 2\cos(x)\,dx

, where

a=\frac{\pi}{3}

and

b=\frac{\pi}{2}

.

(A)

1-\frac{\sqrt3}{2}

(B)

\frac{\sqrt3}{2}-1

(C)

2-\sqrt3

(D)

\sqrt3-2

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer C

1 mark

ANSWER

C —

2-\sqrt3

Worked solution

\displaystyle\int_{\pi/3}^{\pi/2}2\cos x\,dx=[2\sin x]_{\pi/3}^{\pi/2}=2-\sqrt3

, so option C.

Selects option C.

[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