Question

Encontre a área S, limitada por y = x^2 + 1, y = x + 3 e y = x + 7.

Answer 1

Resposta:

y = x²+ 1,  y = x + 3 e y = x + 7

$\int\limits^3_{-2} {x+7-(x^2+1)} \, dx - \int\limits^2_{-1} {x+3 -(x^2+1)} \, dx$

$\int\limits^3_{-2} {-x^2+x+6} \, dx - \int\limits^2_{-1} {-x^2+x+2} \, dx$

$\left[\begin{array}{c}\frac{-x^3}{3} +\frac{x^2}{2} +6x\\\end{array}\right] \limits^3_{-2} - \left[\begin{array}{c}\frac{-x^3}{3} +\frac{x^2}{2} +6x\\\end{array}\right] \limits^2_{-1}$

S= -3³/3+3²/2+6*3+(-2)³/3-(-2)²/2-6*(-2) + 2³/3-2²/2-6*2-(-1)³/3+(-1)²/2+6*(-1)

S=13/3 unidade de área