Question

Find the length of the arc of the curve of 9y ^ 2 = (x ^ 2 + 2) ^ 3 from the point where x = 0 to the point where x = 2 .

Accepted Answer

ext{From the given question }\ y=\sqrt{\frac{(x^2+2)^3}{9}}\
y=\frac{(x^2+2)^{\frac{3}{2}}}{3}\ 	ext{Integrating } y 	ext{ from
} 0 	ext{ to } 2\
\frac{1}{3}\int_0^2(x^2+2)^\frac{3}{2}dx=\frac{1}{4}(x\sqrt{(x^2+2)}(x^2+5)+6\sinh^{-1}(\frac{x}{\sqrt{2}})\Biggr|_0^2\
=12.742

Question #244148

Expert's answer

Answer in progress...