calculus homework help please

Question

A radar gun was used to record the speed of a swimmer (in meters per second) during selected times in the first 2 seconds of a race. Use a trapezoidal sum with 4 intervals to estimate the distance the swimmer covered during those 2 seconds. Give a 2 decimal place answer and include units. 

t	0	0.4	1.0	1.5	2
v(t)	0	4	7.2	8.6	9.0

I am getting 5.49 m, but I'm not sure if it is right

Answer 1

Trapezoid approach means approximating Integral of vdt = d as a sum of trapezoids.

Let's call the earlier velocity v_E and the later velocity v_L Each trapezoid has the "area" (v_E+v_L)/2 * (Δt). Add up the 4 trapezoids to get the integral.

Notice that you can't use the overall trapezoidal rule because the delta t's vary for each interval as you've written it. (v₀/2 +v₁+v₂+v₃+v₄/2)*Δt for constant delta t)

(you might want to check if the time isn't .5 instead of .4)

Good luck. The answer is closer to 12 m