# Thread: [SOLVED] distance travelled- integration

1. ## [SOLVED] distance travelled- integration

How's the best way to approach this using integrals some way or the other? I am confused...

A rocket takes off in a path described by the equation $\displaystyle y= \frac{2}{3}(x^2 - 1)^\frac{3}{2}$. Find the distance travelled by the rocket (rounded to the nearest km) for $\displaystyle x= 4.6 km$, to $\displaystyle x= 6.7km$

2. Originally Posted by Ife
How's the best way to approach this using integrals some way or the other? I am confused...

A rocket takes off in a path described by the equation $\displaystyle y= \frac{2}{3}(x^2 - 1)^\frac{3}{2}$. Find the distance travelled by the rocket (rounded to the nearest km) for $\displaystyle x= 4.6 km$, to $\displaystyle x= 6.7km$
Would the distance traveled by the rocket be the length of the curve from x=4.6 to x=6.7?

3. Originally Posted by ione
Would the distance traveled by the rocket be the length of the curve from x=4.6 to x=6.7?
Well this is what i was unsure about...

4. but i tried it and i got a solution of 134km.. is that about correct? or totally off...?

5. Originally Posted by Ife
but i tried it and i got a solution of 134km.. is that about correct? or totally off...?
That's what I got