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Integration and applications of integration — Question 9

QCAA 2024, Paper 1 · 1 mark

Q9 · 2024 · Technology-freeSimple familiar1 mark

QUESTION 9

Use a suitable double-angle identity to determine

\displaystyle\int 2\sin^2(x)\,dx

.

(A)

x-2\sin(2x)+c

(B)

x+2\sin(2x)+c

(C)

x-\dfrac{\sin(2x)}2+c

(D)

x+\dfrac{\sin(2x)}2+c

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer C

1 mark

ANSWER

C

Worked solution

Since

2\sin^2x=1-\cos2x

, integration gives

x-\frac12\sin2x+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

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