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JAMB Mathematics 2018 Paper

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Question : 49

Total: 62

Evaluate ∫

_{1}^{2}

\frac{5}{x}

dx

1.47
2.67
3.23
3.47

Solution:

Concept:

The integral of

\frac{1}{x}

is

\ln x

, and a constant factor can be taken outside the integral.

Explanation:

Start with the given definite integral:

\displaystyle \int_{1}^{2} \frac{5}{x}\,dx = 5\int_{1}^{2}\frac{1}{x}\,dx

.

Use the standard rule

\int \frac{1}{x}\,dx = \ln x

.

So

5\int_{1}^{2}\frac{1}{x}\,dx = 5\left[\ln x\right]_{1}^{2}

.

Evaluate at the limits:

5(\ln 2 - \ln 1)

.

Since

\ln 1 = 0

, the value is

5\ln 2

.

Using

\ln 2 \approx 0.6931

, we get:

5 \times 0.6931 = 3.4657 \approx 3.47

.

Answer:

3.47

This is option D.

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