Question

calcule a área da região limitada pelas curvas $y=x^{2} -x^4 \\ e \\ y=x^{2} -1$

Answer 1

$A = \displaystyle\mathsf{2\int\limits_{0}^{1}({x}^{2}-{x}^{4}-({x}^{2}-1))dx} \\\mathsf{ = 2 \int \limits_{0}^{1}(1 - {x}^{4})dx }$

$A= \left[2x-\dfrac{2}{5}{x}^{5}\right] _{0}^{1}$

$\mathsf{A=2-\dfrac{2}{5}=\dfrac{8}{5}\,u.a}$