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Question

Find the area of the region enclosed by parabola x2=y, the line y=x+2 and the xaxis.

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Solution

Let's find the point of intersection of curve y=x2 & y=x+2 i.e., finding A & B points
x2=yx2=x+2x2x2=0(x2)(x+1)=0x=1,2y=1,4
So A(1,1) and B(2,4)
Required Area = Area of trapezium ABCDArea of AOBCD
Now, Area of trapezium=12×(sum of parallel sides)×height
=12×(1+4)×3
=152units
Area under AOBCD is
21x2dx=x3321=3
Area required =1533=1562=92units.

1222926_1383209_ans_81b5bc1272dc4b8588a95009486dcd08.png

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