parametric equations

[jaclyncool7]

What is the length of the curve with parametric equations x= (t+4)^2, y=4(t+4)^2 between the points corresponding to t=4 and t=7?

 

[galactus]

Use the arc length formula:

$\displaystyle \int_{a}^{b}\sqrt{\left(\frac{dx}{dt}\right)^{2}+\left(\frac{dy}{dt}\right)^{2}}dt$

Find the derivative of x, square it. Find the derivative of y, square it. Plug it all in and integrate.

You get:

$\displaystyle \int_{4}^{7}\sqrt{68(t+4)^{2}}dt$

Now, finish?.