Question

Find the area of the region bounded by the curve y2=x and the lines x=1,x=4 and the x-axis

Answer 1

The area of the region bounded by the curve y2= x, the lines, x=1 and x = 4,and the x-axis is the area ABCD.

Area of ABCD =$\int^4_1ydx$

=$\int^4_1\sqrt xdx$

=$\bigg[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\bigg]$

=$\frac{2}{3}\bigg[(4)^{\frac{3}{2}}-(1)^{\frac{3}{2}}\bigg]$

=$\frac{2}{3}$[8-1]

=$\frac{14}{3}$ units