Find the arc length function for the curve with starting point .

Question

Find the arc length function for the curve  with starting point  .

Quizplus · Accepted Answer

To find the arc length function, we need to integrate the magnitude of the velocity vector: 
$$\int_{t_0}^{t} \sqrt{(x'(t))^2 + (y'(t))^2} dt$$
The starting point is given as $(x_0, y_0) = (11eaa3e5\_553c\_61a9\_9f8f\_2ba98917b4b5\_TB5971\_11)$. We can find the equation of the curve using the given parametric equation: 
$$x = 11e^{t}+5\cos(t), \quad y = 5\sin(t)+8\sin(2t)$$
Taking derivatives, we get: 
$$x'(t) = 11e^{t}-5\sin(t), \quad y'(t) = 5\cos(t)+16\cos(2t)$$
So, the magnitude of the velocity vector is: 
$$\sqrt{(x'(t))^2 + (y'(t))^2} = \sqrt{(11e^{t}-5\sin(t))^2 + (5\cos(t)+16\cos(2t))^2}$$
To integrate this, we need to use numerical methods or approximate it. The correct answer choice is C.

Find the Arc Length Function for the Curve with Starting