Question

Find the area of the figure bounded by the following curves
y = $(x-1{)}^2,$+ y = 0, x = 2, x = 3.

Answer 1

$y={(x-1)}^2,y=0,x=2$ and $x=3$

At $x=2$ $y={(2-1)}^2=1$

At $x=3y={(3-1)}^2=2^2=4$

Area under curve

${\int }_2^3{(x-1)}^{2}dx$

$=\frac{{(x-1)}^3}{3}{]}_2^3$

$=\frac{2^3}{3}-\frac{1}{3}$

$=\frac{8}{3}-\frac{1}{3}=\frac{7}{3}$ (Answer)