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Integration and applications of integration — Question 5

QCAA 2020, Paper 1 · 1 mark

Q5 · 2020 · Technology-freeSimple familiar1 mark

QUESTION 5

Determine

\displaystyle \int 4x(3x^2+5)^3\,dx

.

(A)

\frac16(3x^2+5)^4+c

(B)

\frac23(3x^2+5)^4+c

(C)

2(3x^2+5)^2+c

(D)

72x^2(3x^2+5)^2+c

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer A

1 mark

ANSWER

A

Worked solution

Let

u=3x^2+5

, so

du=6x\,dx

and

4x\,dx=\frac23du

. Then

\int4x(3x^2+5)^3dx=\frac23\int u^3du=\frac16u^4+c

.

Selects option A.

[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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