Question

Determine a área limitada pela região sombreada.

Escolha uma:
A. 1/6

B. 1/2

C. 5/6

D. 6
E. 1

Answer 1

Resposta:

Letra C

Explicação passo a passo:

y = x² e y = 2 - x

$A=\displaystyle\int_{0}^{1}(x^2-0)dx+\displaystyle\int_{1}^{2}(2-x-0)dx$

$A=\frac{x^3}{3} \left ]{ {{1} \atop {0}} \right.+[2x-\frac{x^2}{2}\left ]{ {{2} \atop {1}} \right. \\\\A=\frac{1}{3} -\frac{0^3}{3} +[(2.2-\frac{2^2}{2}-(2.1-\frac{1^2}{2})] \\\\A=\frac{1}{3} +[4-2-(2-\frac{1}{2}) ]\\\\A=\frac{1}{3} +(2-\frac{3}{2})\\\\A=\frac{1}{3}+\frac{1}{2} \\\\A=\frac{2+3}{6}\\\\A=\frac{5}{6}$