panjang busur kurva y=2/3 x√x dari x=0 sampai x=8 adalah

[tex]
\text{Panjang busur kurva }\\
S=\int_0^8{\sqrt{\left(\frac{dy}{dx}\right)^2+1}}dx\\
=\int_0^8{\sqrt{\left(\sqrt{x}\right)^2+1}}dx\\
=\int_0^8{\sqrt{x+1}}dx\\
=\int_0^8{\sqrt{x+1}}d(x+1)\\
=[\frac{2}{3}(x+1)^{\frac{3}{2}}]_0^8\\
=\frac{2}{3}(8+1)^{\frac{3}{2}}-\frac{2}{3}(0+1)^{\frac{3}{2}}\\
=\frac{2}{3}\cdot27-\frac{2}{3}\cdot1\\
=\frac{52}{3}
[/tex]