Calculus BC Need Help ASAP Please!

Question

 

For an object whose velocity in ft/sec is given by v(t) = -2t² + 4, what is its distance travelled, in feet, on the interval t = 0 to t = 2 secs? (5 points)

Answer Choices:

	4.876
	2.667
	9.752
	2.438

Answer 1

To solve this, you should know that distance is the integral of velocity by definition.

In equation form:

distance = integral(-2t²+4) from t=0 to t=2

= -(2/3)t³ +4t

= -(2/3)2³ +4*2 - (-(2/3)*0³ +4*0)

= -(2/3)*8 + 8 - (0+0)

= 2.667