Solve the attached problem 

$$L=\int_a^b \sqrt{1+(f'(x))^2}dx=\int_0^3\sqrt{1+(2x(x^2-1)^{1/2})}dx=\int_0^3\sqrt{1+4x^2(x^2-1)}dx$$
$$=\int_0^3\sqrt{4x^4-4x^2+1}dx=\int_0^3\sqrt{(2x^2-1)^2}dx=\int_0^3 2x^2-1 dx$$
$$=\frac{2}{3}x^3-\frac{1}{2}x^2|_0^3=\frac{2}{3}3^3-\frac{1}{2}3^2=18-\frac{9}{2}=\frac{27}{2}.$$