# Exam-Style Questions on Differentiation Integration

## Problems on Differentiation Integration adapted from questions set in previous exams.

### 1.

IB Standard

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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