Coordinate of P is (1,1) and the coordinate of Q is (2,0). What is the area of the area bounded by the curve #y=2x-x^2#, the straight line #x+y=2# and the y-axis?

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1 Answer
Noah G
Mar 25, 2018

The area is #5/6# square units.

Explanation:

We want to integrate on #(0, 1)#. You can see that the linear function is above the quadratic function therefore our area equation will be

#A = int_0^1 2 - x - (2x - x^2) dx#

#A = int_0^1 2 - x -2x + x^2 dx#

#A = int_0^1 x^2 - 3x + 2 dx#

#A = [1/3x^3 - 3/2x^2 + 2x]_0^1#

#A = 1/3(1)^3 - 3/2(1)^2 + 2(1)#

#A = 1/3 - 3/2 + 2#

#A =5/6#

Hopefully this helps!

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