Question

Consider the curve x=t^(2) , y= t^(3) from 0 ≦ t ≦ 2

a) Sketch the curve.
b) Find the length of the arc of the curve that lies between (1,1) and (4,8).

Please help me solving this qs!

Answer 1

You good on sketching the curve?

Answer 2

yes!

Answer 3

Okay, for the next part, the arc length can be found using the integral formula,
\[L=\int_CdS=\int_a^b\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}~dt\]

Answer 4

Ok

Answer 5

\[L=\int_1^2\sqrt{4t^2+9t^4}~dt\]
Might require a trig sub...

Answer 6

Or rather not, a simple algebraic sub will do the trick, after some preliminary rewriting.

Answer 7

Alright !

Answer 8

Thanks

Answer 9

yw