# Math Help - length of the given curve

1. ## length of the given curve

one of my HW problems is to find the arc length of the given curve for $x=t^2, y=(3^{1/2}4/3)t^{3/2}, z=3t, 1 <= t <= 4$

now i have the definite integral that goes from 1 to 4, with the equation $(4t^2 + 12t + 9) dt$.

but how do I solve this integral? it seems too hard

2. Originally Posted by Arez
one of my HW problems is to find the arc length of the given curve for $x=t^2, y=(3^{1/2}4/3)t^{3/2}, z=3t, 1 <= t <= 4$

now i have the definite integral that goes from 1 to 4, with the equation $(4t^2 + 12t + 9) dt$.

but how do I solve this integral? it seems too hard
$
l=\int_1^4 \sqrt{\left(\frac{\partial x}{\partial t}\right)^2+\left(\frac{\partial y}{\partial t}\right)^2+\left(\frac{\partial z}{\partial t}\right)^2} \ dt \ = \ \int_1^4 \sqrt{4t^2+12t+9} \ dt \ = \ \int_1^4 (2t+3) \ dt
$