Question 7: Integration Problem

00:00 6 marks

7. [Maximum mark: 6]

(a) Find \(\int (2x^3 + \frac{3}{x^2} – 5) dx\). [3]
(b) Evaluate \(\int_1^e \frac{2}{x} dx\). [3]

Part a

5 minutes 3 marks

Question

Find \(\int (2x^3 + \frac{3}{x^2} – 5) dx\). [3]

Hint Hint

Hint

Separate the integral into three parts and apply the power rule to each term. Rewrite \(\frac{3}{x^2}\) as \(3x^{-2}\).

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Complete Answer

\(\frac{1}{2}x^4 – \frac{3}{x} – 5x + C\)

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Part b

5 minutes 3 marks

Question

Evaluate \(\int_1^e \frac{2}{x} dx\). [3]

Hint Hint

Hint

Remember that \(\int \frac{2}{x} dx = 2\ln|x|\) and apply the definite integral from 1 to e.

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