Question

Valor do volume do sólido de rotação limitado pela curva y=x³ e pelas retas y=8 e y=0

Answer 1

Resposta:

$V=\frac{\pi *8^7}{7} u^3$

Explicação passo a passo:

$V=\pi \displaystyle\int_{a}^{b}[f(x)]^2dx\\\\V=\pi \displaystyle\int_{0}^{8}(x^3)^2dx\\\\V=\pi \displaystyle\int_{0}^{8}x^6dx\\\\V=\pi *\frac{x^7}{7} \left ]{ {{8} \atop {0}} \right. \\\\V=\frac{\pi }{7}*(8^7 -0^7)\\\\V=\pi *\frac{8^7}{7} \\\\V=\frac{\pi *8^7}{7}\\\\V=941.199,62 u^3$