# Exam-Style Question on Integration

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 381. This question is similar to one that appeared on an A-Level paper. The use of a calculator is allowed.

(a) Express the algebraic fraction

$$\frac{6x^2 - 47x + 49}{(5-x)(1-2x)}$$

in the form

$$A + \frac{B}{5-x} + \frac{C}{1-2x}$$

where $$A$$, $$B$$ and $$C$$ are integers.

(b) Hence show that the following integral equates to 3.03 correct to three significant figures.

$$\int^{0.25}_0 \frac{6x^2 - 47x + 49}{(5-x)(1-2x)} dx$$
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