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I have done questions involving area between curve and $x$-axis / $y$-axis or between two curves but here the term is $xy=a^2$ and I am confused how to solve it using concept of definite integration . If someone guide me how to start it will be great

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    $\begingroup$ HINT: $xy=a^2\implies y=\frac{a^2}{x}$ $\endgroup$ – nathan.j.mcdougall Sep 12 '15 at 18:42
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    $\begingroup$ Thanks i got the answer 2a^2(log2) by integrating it from a to 4a . $\endgroup$ – Dungeon_master Sep 12 '15 at 18:52
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Since $a > 0$, then $x \neq 0$ and your formula $xy = a^2$ is equivalent to $y = \frac{a^2}{x}$. Then of course $y$ is a function of $x$ and $y = f(x) = \frac{a^2}{x}$ for all $x \neq 0$. Now you can calculate the area you are interested in like this:

$$\int_{a}^{4a} f(x)dx$$

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  • $\begingroup$ Thanks , i got the answer with a little help of @nathan.j.mcdougall $\endgroup$ – Dungeon_master Sep 12 '15 at 18:57

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