Question

Evaluate :
${\int }_0^4(x+x^{3/2}dx)$

Answer 1

$I={\int }_0^4(x+x^{3/2})dx$

$=\frac{x^2}{2}+\frac{x^{3/2+1}}{\frac{3}{2}+1}{]}_0^4$

$=\frac{x^2}{2}+\frac{2x^{5/2}}{5}{]}_0^4$

$=\frac{16}{2}+\frac{2}{5}\times 2^5-0-0$

$=8+\frac{2^6}{5}$

$=8+\frac{64}{5}$

$=\frac{40+64}{5}=\frac{104}{5}$