A particle moves along the x-axis. The velocity of the particle at time t is −2t+8 . What is the total distance traveled by the particle from t=1 to t=6?

13

Step-by-step explanation:

The velocity is given by:

And the total distance given the velocity is given by:

So, the total distance traveled by the particle from t = 1 to t = 6 will be:

The absolute value tells us that:

So, split the integral into two parts:

Integrate:

Evaluate:

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.