Calc FRQ
david_kungpao12
CALCFRQ.docxSHOW ALL WORK AND CALCULATIONS
1. Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval. Give three decimal places in your answer.
2. Explain, using a graph of f(x), what the Riemann sum in Question #1 represents.
3. Express the given integral as the limit of a Riemann sum but do not evaluate: .
4. Use the Fundamental Theorem to evaluate .
(Your answer must include the antiderivative.)
5. Use a graph of the function to explain the geometric meaning of the value of the integral.
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A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position at time t = 0 sec is 1 meter right of zero, that is, s(0) = 1.
1. The average velocity over the interval 0 to 8 seconds
2. The instantaneous velocity and speed at time 5 secs
3. The time interval(s) when the particle is moving right
4. The time interval(s) when the particle is
a. going faster
b. slowing down
5. Find the total distance the particle has traveled between 0 and 8 seconds
