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Area between two curves challenge

Let  I ~I~ be the blue shaded region between the graphs of
f(x)=212x   \qquad f(x)=2-\dfrac12x~~~and   g(x)=x2~~~g(x)=\sqrt{\dfrac x2}
and let  II ~II~ be the red shaded region between the graph of
  g(x)=x2  \qquad ~~g(x)=\sqrt{\dfrac x2}~~and the  x~x-axis for  x[0,2]~x\in[0,2]
as shown in the figure.
Match each region with the definite integral that gives its area.
Region
Definite integral for area
  • II
  • IIII
  • I+III+II
  • 02x2dx\displaystyle \int_{0}^2\sqrt{\dfrac x2}\,dx
  • 02(2x2x2)dx\displaystyle \int_{0}^2\Big(2-\dfrac x2-\sqrt{\dfrac x2}\,\Big)\,dx
  • 02(2x2)dx\displaystyle \int_{0}^2\Big(2-\dfrac x2 \Big)\,dx