A biker is slowing down according to the following table of velocities:
Time (secs) 0 1 2 3 4
Velocity (feet/sec) 25 20 16 12 10
Approximate the distance traveled, in feet, during these 4 seconds using 4 rectangles and a Left Riemann Sum.
A. 20.75
B. 58 <-----My choice
C. 73
D. 83
My work: s(4) = ∫04 v(t) dt ≈ [f(1) + f(2) + f(3) + f(4)]Δt = [20 + 16 + 12 + 10](1) = 58 feet.
AM i right? Thank you! :)
It's 73
trust bro
no, you used a right Riemann sum.
Oh ok. Got it
Yes, you are correct! You have correctly applied the Left Riemann Sum method to approximate the distance traveled.
The Left Riemann Sum is an approximation method used to estimate the area under a curve by dividing the interval into equal subintervals and taking the left endpoint of each subinterval as the height for a rectangle. In this case, you have divided the interval [0, 4] into four equal subintervals, with Δt = 1.
Then, you have calculated the sum of the velocities at time 1, 2, 3, and 4, and multiplied it by Δt (which is 1 in this case) to find the total area under the curve. This gives you an approximate distance traveled of 58 feet.
Therefore, your choice of option B is correct. Well done!