QuestionCurrent Attempt in Progress The velocity of a car is $f(t)=4 t$ meters $/ \mathrm{sec}$. Use a graph of $f(t)$ to find the exact distance traveled by the car, in meters, from $t=0$ to $t=6$ seconds.
The distance traveled by the car is $\square$ meters. eTextbook and Media

Studdy Solution
Evaluate the integral:
$$\int 4t \, dt = 2t^2 + C$$
Now, calculate the definite integral from $t = 0$ to $t = 6$:
$$\int_{0}^{6} 4t \, dt = \left[ 2t^2 \right]_{0}^{6}$$
$$= 2(6)^2 - 2(0)^2$$
$$= 2(36) - 0$$
$$= 72$$
The exact distance traveled by the car is:
$$\boxed{72} \text{ meters}$$