Question

Como resolvo? $\int\limits^0_3 { \sqrt{1+ x^{4}+ 2 x^{2} } } \, dx$

Answer 1

Olá, JuuhRezende.

$\int\limits^0_3 { \sqrt{1+ x^{4}+ 2 x^{2} } } \, dx =\\\\= \int\limits^0_3 { \sqrt{x^{4}+ 2 x^{2}+1 } } \, dx =\\\\ =\int\limits^0_3 { \sqrt{(x^{2}+1)^2 } } \, dx =\\\\=\int\limits^0_3 { x^{2}+1} } \, dx =\\\\ =\left\frac{x^3}{3}\right|\limits_3^0+\left x\right|\limits_3^0=\\\\=-\frac{27}{3}-3=\\\\=\boxed{-12}$