Methods2024 NHT Exam 1 · Q8Tech-free4 marks

Antiderivative and average value of a reciprocal square root

Let $f:\left(-\frac{1}{3}, \infty\right) \to R,\ f(x) = \frac{1}{\sqrt{3x+1}}$ .

Find an anti-derivative for $f(x)$ .

1 mark

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The average value of the function, $f$ , over $0 \le x \le m$ is $\frac{1}{3}$ .

Find the value of $m$ .

3 marks

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