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Paper 2 · June 2008 · Integration

The region enclosed by $y=\dfrac{a}{x}$ , $y=\dfrac12$ , the $y$ -axis and $y=2$ has exact area $a\ln 4$ , where $a$ is a positive integer. Find the minimum value of $a$ for which this area exceeds 100.

Model answer

73

Explanation

a\ln 4>100

gives

a>\dfrac{100}{1{,}3863}=72{,}13\ldots

, and since

a

is a positive integer the least such value is

a=73

.

Derived from ZIMSEC Mathematics Paper 2, June 2008, Q1

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