query: Area between two functions is the same as area between the inverse functions
positive_passages.docid: 144192
positive_passages.text: Showing $\int_{\mathbb R} \mid F(x)-G(x)\mid dx = \int_0^1 \mid F^{-1}(u)-G^{-1}(u)\mid du$ with $F$, $G$ CDF functions
negative_passages.docid: 62781
negative_passages.text: InverseFunction and Plot them
negative_passages.docid: 104701
negative_passages.text: Find the functions for which the area of the triangle made by tangent at a point is independent of the point
negative_passages.docid: 81679
negative_passages.text: Why is $f(4)$ the area under $f'(x)$ specifically from $0$ to $4$ and not for ex from $1$ to $4$ or $2$ to $4$?
negative_passages.docid: 2635
negative_passages.text: equality of two operators...
negative_passages.docid: 115131
negative_passages.text: Proof that sum of integrals of same function on adjacent intervals equals the integral over both intervals
negative_passages.docid: 35589
negative_passages.text: Exact area using limits and Riemann sum
negative_passages.docid: 144439
negative_passages.text: For a $C^1$ function, the difference $|{g'(c)} - {{g(d)-g(c)} \over {d-c}} |$ is small when $|d-c|$ is small
negative_passages.docid: 134880
negative_passages.text: Is there a difference between $y(x)$ and $f(x)$
negative_passages.docid: 2022
negative_passages.text: Filling area under a function
negative_passages.docid: 124374
negative_passages.text: A bijective function between a square and its side
negative_passages.docid: 11022
negative_passages.text: filling area between 2 functions, with shading
negative_passages.docid: 127953
negative_passages.text: Integral of periodic function over the length of the period is the same everywhere
negative_passages.docid: 124808
negative_passages.text: How to find inverse of function?
negative_passages.docid: 95067
negative_passages.text: Area of the Limiting Polygon
negative_passages.docid: 141863
negative_passages.text: If the imaginary part of an entire function is never zero, the function is constant
negative_passages.docid: 126698
negative_passages.text: measurability of a function -equivalent conditions