Further integration — Question 31

Original QCE Vault practice · 3 marks

Q31 · Practice questionTechnology-freeSimple familiar3 marks

QUESTION 31 (3 marks)

Evaluate

\displaystyle\int_0^1\frac{4x}{x^2+1}\,dx

WORKED SOLUTION

3 marks

ANSWER

2\ln2

Worked solution

Let

u=x^2+1

, so

du=2x\,dx

. The integral becomes

2\int_1^2du/u=2\ln2

Recognises or applies the substitution

u=x^2+1

[1 mark]

Obtains

2\ln(x^2+1)

as an antiderivative.

[1 mark]

Evaluates the bounds to obtain

2\ln2

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.

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