Question

Draw a rough sketch of the curve $y=\sqrt{x-1}$ in the interval [1, 5]. Find the area under the curve and batween the lines x = 1 and x = 5.

Answer 1

Given equation of the curve is $y=\sqrt{x-1}$

$\Rightarrow y^2=x-1$

$\therefore$ Area of shaded region, $A={\int }_1^5(x-1{)}^{\frac{1}{2}}dx={\left[\frac{2.(x-1{)}^{\frac{3}{2}}}{3}\right]}_1^5=[\frac{2}{3}.(5-1{)}^{\frac{3}{2}}-0]=\frac{16}{3}squnits$