Question

Am nevoie de ajutor la acest exercițiu...
Mulțumesc anticipat!

Answer 1

$\text{Daca } f(a) = c \text{ si }f(b) = d\\ \\ \displaystyle \boxed{\int_{a}^bf(x)\, dx+\int_{c}^d f^{-1}(y)\, dy = bd-ac}\rightarrow \text{Teorema lui Laisant}\\ \\ \text{In cazul acesta:}\\ \\ f(a) = \alpha\text{ si }f(b) = \beta \\ \\\int_{a}^bf(x)\, dx+\int_{\alpha}^\beta f^{-1}(y)\,dy = \int_{a}^bf(x)\, dx+\int_{\alpha}^\beta g(y)\, dy= b\beta - a\alpha \\ \\ \Rightarrow b)\text{ corect}$