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.
Well it is called homework HELP
To evaluate the Riemann sum for the function f(x) = x^3 - 6x, with six subintervals and using right endpoints, we can follow these steps:
1. Calculate the width, or the Δx, of each subinterval:
Δx = (b - a) / n
where a is the lower limit (0), b is the upper limit (3), and n is the number of subintervals (6).
Δx = (3 - 0) / 6 = 0.5
2. Determine the right endpoints for each subinterval:
The right endpoints can be found by adding the width of each subinterval to the left endpoint of that subinterval.
Right Endpoint 1: x1 = 0 + 0.5 = 0.5
Right Endpoint 2: x2 = 0.5 + 0.5 = 1
Right Endpoint 3: x3 = 1 + 0.5 = 1.5
Right Endpoint 4: x4 = 1.5 + 0.5 = 2
Right Endpoint 5: x5 = 2 + 0.5 = 2.5
Right Endpoint 6: x6 = 2.5 + 0.5 = 3
3. Compute the value of the function at each right endpoint:
Evaluate f(x) = x^3 - 6x at each right endpoint.
f(x1) = (0.5)^3 - 6(0.5) = -2.625
f(x2) = (1)^3 - 6(1) = -5
f(x3) = (1.5)^3 - 6(1.5) = -6.375
f(x4) = (2)^3 - 6(2) = -4
f(x5) = (2.5)^3 - 6(2.5) = -1.625
f(x6) = (3)^3 - 6(3) = 0
4. Calculate the Riemann sum by summing the products of the width and the function value at each right endpoint:
Riemann Sum = Δx * (f(x1) + f(x2) + f(x3) + f(x4) + f(x5) + f(x6))
Riemann Sum = 0.5 * (-2.625 + (-5) + (-6.375) + (-4) + (-1.625) + 0)
Riemann Sum = 0.5 * (-19.625)
Riemann Sum = -9.8125
Therefore, the Riemann sum for the given function, with six subintervals and using right endpoints, is approximately -9.8125.
there are various Riemann sum calculators online.
Or heck, drag out your calculator and do the math.
Where do you get stuck?
All those posts looks like a homework dump to me.