Question

The value of ${\int }_0^3{x}^{5/2}dx$ is

• A. $\frac{54}{7}$
• B. $\frac{\sqrt{3}}{7}$
• C. $\frac{54\sqrt{3}}{7}$
• D. None of these

Answer 1

Answer: (C)

$\frac{54\sqrt{3}}{7}$

${\int }_0^3{x}^{5/2}dx$

$\int x^{n}dx=\frac{x^{n+1}}{n+1}+c$

${\int }_0^3{x}^{5/2}dx=\frac{x^{\frac{5}{2}+1}}{\frac{5}{2}+1}{|}_0^3$

$=\frac{2x^{7/2}}{7}{|}_0^3\frac{2(3{)}^{7/2}}{7}-0=\frac{54\sqrt{3}}{7}$