Integration Problem

00:00 6 marks

7. (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

Integrate each term separately: use the power rule for $2x^3$ and rewrite $\frac{3}{x^2}$ as $3x^{-2}$ before integrating.

Answer Answer
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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

Recall that $\int \frac{1}{x} dx = \ln|x|$, so the antiderivative here is $2\ln|x|$.

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Complete Answer

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