Use the Left and Right Riemann Sums with 100 rectangles to estimate the (signed) area under the curve of y=−6x+8 on the interval [0,50]. Write your answer using the sigma notation.

Answer 1

∆x = 50/100 = 1/2
so the Left Sum area is the sum of a lot of rectangles of height f(x) and width ∆x
99
∑ f(k*∆x)*∆x = ∑(-6k∆x+8)*∆x = ∑(-6k/2+8)(1/2) = ∑(-3k/2 + 8)
0

For the Right sum, sum over k=1..100 instead