This question will have you evaluate ∫ 0
6
​
8−2xdx using the definition of the integral as a limit of Riemann sums. i. Divide the interval [0,6] into n subintervals of equal length Δx, and find the following values: A. Δx= B. x 0
​
= C. x 1
​
= D. x 2
​
= E. x 3
​
= F. x i
​
= ii. A. What is f(x) ? Evaluate f(x i
​
) for arbitrary i. B. Rewrite lim n→[infinity]
​
∑ i=1
n
​
f(x i
​
)Δx using the information above. C. Evaluate first the sum, then the limit from the previous part. You may find the following summation formulas useful: ∑ i=1
n
​
c=c⋅n,∑ i=1
n
​
i= 2
n(n+1)
​
,∑ i=1
n
​
i 2
= 6
n(n+1)(2n+1)
​
,∑ i=1
n
​
i 3
=[ 2
n(n+1)
​
] 2
.