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Area under this curves will be 15 square units
to get the answer first find the intersecting points(3,0) of both curves then integrate the both equations then put the limits 0 to 3 and solve it
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The area of the region bounded by y=2x-x^2 and y=x-2.y=2x−x^2 and y=x−2.   intesect when  2x−x^2 =x−2
→x² −x −2 =0  i.e  (x−2)(x+1)=0
I.e either x=2 or x= −1
hence Area of the region bounded by  y=2x−x^2 and y=x−2
is A=∫ (from x= −1_to x=2) of  {(2x−x^2) −(x−2)}dx 
A=∫ (from x= −1_to x=2) of  {(x−x^2+2) }dx 
A= {(x²−x³/3+2x)} (from x= −1_to x=2) 
= {(2²−2³/3+2×2)} − {(−1)²−(−1)³/3+2(−1)}
= {(4−8/3+4)} − {1+1/3−2)}
= {(16/3)} +{2/3} = 6 sq. units 

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