Question

Find the value of $k$ if ${\int }_4^9\sqrt{x}dx$ = $\frac{k}{3}$

Answer 1

${\int }_4^9\sqrt{x}dx$

$={[x^{3/2}\times \frac{2}{3}]}_4^9$

$=\frac{2}{3}[9^{3/2}-4^{3/2}]$

$=\frac{2}{3}[27-8]$

$=\frac{38}{3}$

Now $\frac{k}{3}=\frac{38}{3}$

$\therefore k=38$