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Integration and applications of integration — Question 8

QCAA 2022, Paper 1 · 1 mark

Q8 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 8

Use the substitution

u=\tan(x)

to determine

\displaystyle \int \tan(x)\sec^2(x)\,dx

.

(A)

\frac12\tan(x)+c

(B)

\frac12\tan^2(x)+c

(C)

\tan(x)+c

(D)

\tan^2(x)+c

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer B

1 mark

ANSWER

B

Worked solution

With

u=\tan x

,

du=\sec^2x\,dx

. Therefore

\int\tan x\sec^2x\,dx=\int u\,du=\frac12u^2+c=\frac12\tan^2x+c

.

Selects option B.

[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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