Calculus please help!

Question

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

Answer Choices:

	1.333
	2.438
	2.667
	-4

Answer 1

1.333

integrate -t^2 + 2 to get -t^3/3 + 2t

evaluate at t=2

-8/3 + 4 = 4/3 = 1.333 rounded to 3 decimals

Answer 2

Displacement s = ∫₀²abs(2 - t²)dt = ∫₀^√2¦_{(2 - t}²)dt + ∫_√2²(t² - 2))dt = (2t - t³/3)₀^√2 + (t³/3 - 2t)_√2² =

2√2 - 2√2/3 + 8/3 - 4 - 2√2/3 + 2√2 = 8√2/3 - 4/3 = 4(2√2 - 1)/3 = 2.4379 = 2.438