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I'm trying to calculate the region enclosed by $y=\frac{1}{x^2}$, $y=x$ and $y=4$ for $x \in [\frac{1}{2}, 4]$ How can I do this?

I know I can use definite integral for this task but I want a general formula that I can apply in WolframAlpha to check my calculations. Something like find area between y=1/x^2, y=x, y=4 from 1/2 to 4 but working. find area between y=1/x^2, y=x, y=4 works and returns (unbounded) as expected but I also need a way to specify interval.

Matt
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The area is $$\int_{1/2}^1 \left(4-\frac{1}{x^2}\right)dx+\int_1^4(4-x)\,dx=\frac{11}{2}.$$

A. Goodier
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  • Thanks, but do you know a command for WolframAlpha that can compute this for some number of functions for any interval? I know I can use definite integral to calculate the area but I'm looking for a command to check my calculations in WolframAlpha e.g. something like find area between y=1/x^2, y=x, y=4 from 0 to 4 (this doesn't work though, just an example). – Matt Jan 13 '18 at 16:33
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    Integrate[4-1/x^2,{x,1/2,1}]+Integrate[4-x,{x,1,4}] – Awnon Bhowmik Jan 13 '18 at 16:37