Question

Find the area of the region bounded by y2=9x, x=2, x=4 and the x-axis in the first quadrant.

Answer 1

The area of the region bounded by the curve,y2=9x,x=2,and x=4,and the x-axis is the area ABCD.

Area of ABCD =$\int^4_2ydx$

=$\int^4_2\sqrt xdx$

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

=$2\bigg[x^{\frac{3}{2}}\bigg]^4_2$

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

=$2[8-2\sqrt2]$

=(16-4$\sqrt2$) units.