Calculating Arc Length for r(t)=(10t^2,2*sqrt(10)*t, ln t) from t=1 to t=8

[Larrytsai]

Homework Statement

Find the arclength of the curve r(t)=(10t^2,2*sqrt(10)*t, ln t)
for 1<=t<=8

Homework Equations

The Attempt at a Solution

i took the derivative of each component of vector r

20t,2sqrt(10),1/t
then i square each term and square root it

int sqrt( 400t + 40 + 1/t^2)dt

i can't integrate this to find out the length tho.

 

[Mark44]

Homework Statement

Find the arclength of the curve r(t)=(10t^2,2*sqrt(10)*t, ln t)
for 1<=t<=8

Homework Equations

The Attempt at a Solution

i took the derivative of each component of vector r

20t,2sqrt(10),1/t
then i square each term and square root it

int sqrt( 400t + 40 + 1/t^2)dt

400t should be 400t².

i can't integrate this to find out the length tho.

If you make the change above, you'll have a perfect square that you can take the square root of.