Mathematics

Problem

Which of the following definite integrals equals the exact area of the region bounded by the curves

x = 4 - y^{2}

and

x = y + 2

for

-1 \le y \le 3

? a)

\displaystyle\int_{-1}^{3}\big[(y+2) - (4 - y^{2})\big]\,dy

\displaystyle\int_{-1}^{1}\big[(4 - y^{2}) - (y + 2)\big]\,dy + \int_{1}^{3}\big[(4 - y^{2}) - (y + 2)\big]\,dy

\displaystyle\int_{-1}^{1}\big[(4 - y^{2}) - (y + 2)\big]\,dy + \int_{1}^{3}\big[(y + 2) - (4 - y^{2})\big]\,dy

\displaystyle\int_{-2}^{1}\big[(4 - y^{2}) - (y + 2)\big]\,dy