Question

qual alternativa corresponde a area destacada na figura abaixo;

Answer 1

Boa noite João!

Solução!

A resolução dessa integral é semelhante a outra,porem essa função tem mais a frente um ponto de intersecção entre a curva e a reta igual a 9,entretanto os intervalos já estão estabelecido[0,1]

$\displaystyle \int_{0}^{1} ( \sqrt{x} ) dx\\\\\\\\\ A=\displaystyle \int_{0} ^{1} ( \sqrt{x} ) dx\\\\\\\\\ A=\displaystyle \int _{0}^{1} ( \frac{(x) ^\frac{1}{2}}{ \frac{1}{2} } ) dx\\\\\\\\\ A= ( \frac{(x)^\frac{1}{2}^{+1} }{ \frac{1}{2}+1 }) ~~\bigg|_{0} ^{1}$


$A= ( \frac{(x)^\frac{3}{2}}{ \frac{3}{2} }) ~~\bigg|_{0} ^{1} \\\\\\\\\ A= ( \frac{ \sqrt{x^{3} } }{ \frac{3}{2} }) ~~\bigg|_{0} ^{1} \\\\\\\\\ A= ( \frac{2}{3} . \sqrt{x^{3}}) ~~\bigg|_{0} ^{1}$


$A= ( \frac{2}{3} . \sqrt{x^{3}}) -( \frac{2}{3} . \sqrt{x^{3}}) \\\\\\\\ A= ( \frac{2}{3} . \sqrt{(1)^{3}}) -( \frac{2}{3} . \sqrt{(0)^{3}}) \\\\\\\\ A= ( \frac{2}{3} . \sqrt{1}) -( \frac{2}{3} . \sqrt{0}) \\\\\\\\ A= ( \frac{2}{3} . 1) -( \frac{2}{3} . 0) \\\\\\\\ A= ( \frac{2}{3} ) -( 0) \\\\\\\\ A= \dfrac{2}{3}~~u.a$


$\boxed{Resposta:A= \dfrac{2}{3}~~u.a~~\boxed{Alternativa~~b}}$


Boa noite!

Bons estudos!