Answer :

Given equations are:

x = 2 ...... (1)


And y2 + 1 = x, x 2 ...... (2)


equation (2) represents a parabola with vertex at (1,0) and passing through (2,0) on x - axis, equation (1) represents a line parallel to y - axis at a distance of 2 units.


A rough sketch is given as below: -


8.PNG


We have to find the area of shaded region.


Required area


= shaded region ABCA


= 2 (shaded region ACDA) ( as it is symmetrical about the x - axis)


(the area can be found by taking a small slice in each region of width Δx, then the area of that sliced part will be yΔx as it is a rectangle and then integrating it to get the area of the whole region)


(As x is between (1,2) and the value of y varies)


(as )



Substitute


So the above equation becomes,



On integrating we get,



On applying the limits we get,




Hence the area enclosed by the curve and the line x = 2 is equal to square units.


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