Question

passo a passo integral definida :
integral (0 a 4) de (4x-x²)dx

Answer 1

Boa noite Matheus!


Solução!


$\displaystyle \int_{0} ^{4}(4x- x^{2})dx\\\\\\\\\ \displaystyle \int_{0} ^{4}(4x- x^{2})dx= \frac{4 x^{2} }{2}- \frac{ x^{3} }{3}=2 x^{2} - \frac{ x^{3} }{3}+c$

$I=\left (2 x^{2} - \dfrac{ x^{3} }{3} \right )-\left ( 2 x^{2}- \dfrac{ x^{3} }{3} \right )\Bigg|_{0} ^{4}\\\\\\\ I=\left (2(4)^{2} - \dfrac{ (4)^{3} }{3} \right )-\left ( 2 (0)^{2}- \dfrac{ (0)^{3} }{3} \right )\\\\\\\ I=\left (2(16)} - \dfrac{ 64}{3} \right )-\left ( 2 (0)- \dfrac{ (0) }{3} \right )\\\\\\\ I=\left( 32} - \dfrac{ 64}{3} \right )-\left ( 0- \dfrac{ (0) }{3} \right )\\\\\\\ I=\left( \dfrac{96- 64}{3} \right )-\left ( \dfrac{ 0-0 }{3} \right )$

$I=\left( \dfrac{32}{3} \right )-\left ( \dfrac{ 0 }{3} \right )\\\\\\\ I=\left( \dfrac{32-0}{3} \right )\\\\\\\ I=\left( \dfrac{32}{3} \right )\\\\\\\\\\\\\\\ \boxed{Resposta:\displaystyle \int_{0} ^{4}(4x- x^{2})dx= \frac{32}{3}}$

Boa noite!

Bons estudos!