Note that is an even function (green line).
P165. Find the area of the region in the xy plane, bounded by the graphs of , x+y = 2 and
The parabola and straight line intersects at (1,1) (we find that by solving the and x+y=2)
Thus the area is found by adding area under parabola (from 0 to 1) and area under straight line (from 1 to 2).
(area under parabola)
area under straight line above ‘x’ axis is the triangle with height 1 unit and base 1 unit (from x=1 to x=2, area under x+y=2)
that area =
Thus total area above x axis (of the required region) is
Now we come to the region below ‘x’ axis.
x+y = 2 and intersect at (4, -2) (found by solving the two equations). We calculate the area under the curve from x=0 to x=4 and subtract from it the area of the triangle with base from x=2 to x=4 and height =2 (hence the area of the triangle to be subtracted is 2 sq unit).
Area under the square root curve is
Delete 2 square unit from this and add the area computed before (above ‘x’ axis).
Area = (ANS)