Question

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.

Answer 1

Answer:

Step-by-step explanation:

Given that $f(x) = x^3-6x$, $0\leq x\leq 3$

Interval length = 3-0 =3

No of intervals= 6

Hence the end points are

$0, 0.5, 1, 1.5, 2, 2.5, 3$

Right end points are

x  0.5 1 1.5 2 2.5 3 total

f(x)  -2.875 -5 -5.625 -4 0.625 9 -7.875

       

Integral value  0.5*(-7.875) -3.9375      

So Riemann sum is -3.9375

= -3.938