Draw a rough sketch of the curve in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5


Squaring both sides


y2 = x – 1


y2 = x – 1 is equation of a parabola


In y2 = x – 1 parabola it is not defined for values of x less than 1 hence the parabola will be to the right of x = 1 passing through (1, 0)


Now observe that in x ≥ 1 and y has to positive because of square root hence x and y both positive hence the parabola will be drawn only in 1st quadrant


We have to plot the curve in [1, 5] so just draw the parabolic curve from x = 1 to x = 5 in 1st quadrant


x = 1 and x = 5 are lines parallel to Y-axis



So we have to integrate from 1 to 5


let us find area under parabolic curve



Integrate from 1 to 5










Hence area bounded = unit2


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