Question

Determine o volume do sólido gerado pela rotação  y =x^2 +1  entre 0 e 1.

Answer 1

$\pi \int\limits^1_0 {(x^2+1)^2} \, dx \\\\=\boxed{\boxed{ \pi \int\limits^1_0 {(x^4+2x^2+1)} \, dx }}$

integrando
$\frac{x^5}{5}+ \frac{2x^3}{3}+x\\\\\ F(1)= \frac{1^5}{5}+ \frac{2*1^3}{3}+1 = \frac{28}{15} \\\\F(0) = 0\\\\\\\\ F(1) - F(0) = \frac{28}{15}$

$\boxed{\boxed{\pi \int\limits^1_0 {(x^4+1)^2} \, dx = \frac{28 \pi }{15} }}$