Line integral problem?

[insanerp]

Evaluate the line integral, where C is the given curve.
?C y^3ds, C:x = t3, y = t, 0 ? t ? 5
after subing in y=t for y^3 and taking the sqrt of the ((partial in respects to x)^2 + (partial in respects to y)^2 ) then did a u sub and reduced my answer to 210937 / 27 what did I do wrong? please help

 

[galactus]

Is that \(\displaystyle \int_{C}y^{3}dx, \;\ x(t)=t^{3}, \;\ y(t)=t, \;\ 0\leq t\leq 5\)

Try \(\displaystyle \int_{0}^{5}t^{3}\cdot 3t^{2}=3\int_{0}^{5}t^{5}dt=\frac{15625}{2}\)

You appear to be very close.

 

[insanerp]

arithmetric error found the correct answer to be 1/54(5626^(3/2)-1), thanks.