The figure shows the region bounded by y =…

The figure shows the region bounded by y = 1/x, the x-axis and the lines x = 1 and x = e^2.

Question 65

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The figure shows the region bounded by $y = \frac{1}{x}$ , the $x$ -axis and the lines $x = 1$ and $x = e^{2}$ . What is its area?

$The graph of y = \frac{1}{x} with the region under it between x = 1 and x = e^{2} shaded, down to the x-axis.$

1 - e^{-2}

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1

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2

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4

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CorrectNot quiteAnswer C

Correct answer: C

The curve stays above the $x$ -axis on $[1, e^{2}]$ , so the area is $\int_{1}^{e^{2}} \frac{1}{x}\,dx$ .
That is $2$ square units.

Ten questions from Definite Integrals & Area, at your own pace.

Ten questions from Definite Integrals & Area, at your own pace.