Q. 55.0( 1 Vote )

Find the area of the region included between y2 = 9x and y = x

Answer :

In y2 = 9x parabola it is not defined for negative values of x hence the parabola will be to the right of Y-axis passing through (0, 0)


And y = x is a straight line passing through origin


We have to find area between y2 = 9x and y = x shown below



To find intersection point of parabola and line solve parabola equation and line equation simultaneously


Put y = x in y2 = 9x


x2 = 9x


x = 9


Put x = 9 in y = x we get y = 9


Hence point of intersection is (9, 9)


area between parabola and line = area under parabola – area under line …(i)



Let us find area under parabola


y2 = 9x


y = 3√x


Integrate from 0 to 9









Now let us find area under straight line y = x


y = x


Integrate from 0 to 9







Using (i)


area between parabola and line = 54 – 40.5 = 13.5 unit2


Hence area bounded is 13.5 unit2


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