Find Distance Covered by Point P on Parametric Curve: 0 to 9

[ILoveBaseball]

Consider the parametric curve given by the equations
$$x(t) = t^2+30t-11$$
$$y(t)=t^2+30t+38$$
How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=9 ?

well since the bounds are already given (0->9), i just need help on setting up the integral. here's what i done:

$$dx/dt = 2t+30$$

my integral:

$$\int_{0}^{9}(t^2+30t+38)*(2t+30)$$

but i get the incorrect answer when i integral it, can someone help me set it up?

 

[ehild]

Consider the parametric curve given by the equations
$$x(t) = t^2+30t-11$$
$$y(t)=t^2+30t+38$$
How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=9 ?

well since the bounds are already given (0->9), i just need help on setting up the integral. here's what i done:

$$dx/dt = 2t+30$$

my integral:

$$\int_{0}^{9}(t^2+30t+38)*(2t+30)$$

but i get the incorrect answer when i integral it, can someone help me set it up?

The distance traveled is

$$\int_{0}^{9}\sqrt{(dx/dt)^2+(dy/dt)^2}dt$$

You either do this integral, or notice that the curve is a straight line.

ehild

 

[Yegor]

What is the formula for calculating curve's length? You have calculated the area under the curve, not the length.

 

[ILoveBaseball]

thank you, i got it correct