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