## Exam-Style Question on Calculus## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 70. This question is similar to one that appeared on an IB Standard paper in 2014. The use of a calculator is not allowed.

Let \(f(x)=\frac{2x}{x^2+3}\)

(a) Use the quotient rule to show that \(f'(x)=\frac{6-2x^2}{(x^2+3)^2}\).

(b) Find \(\int \frac{2x}{x^2+3}dx\).

(c) The area enclosed by the graph of \(f(x)\), the x-axis and the lines \(x=\sqrt3\) and \(x=n\) has an area of \(\ln14\). Find the value of \(n\).

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