Question

encontre a área as curvas y=x^2e y=2x

Answer 1

$x^2=2x\\x^2-2x=0\\x\cdot(x-2)=0\\\\x'=0\\\\x-2=0\\x"=2$

$\int\limits^2_0 {(2x-x^2)} \, dx\\\\\\ \int\limits^2_0 {2x} \, dx - \int\limits^2_0 {x^2} \, dx\\\\\\ \dfrac{2x^2}{2}- \dfrac{x^3}{3}\bigg|_0^2\\\\\\x^2-\dfrac{x^3}{3}\bigg|_0^2\\\\\\4- \dfrac{8}{3}= \dfrac{12-8}{3}= \dfrac{4}{3}\ u.a$

Obs:

u.a => unidade de área
Observe a figura em anexo