Question

If the integral of (x^2 - 2x + 2)dx from 0 to 6 is approximated by three inscribed rectangles of equal width on the x-axis, then the approximation is equal to what?

Answer 1

for a better approximation
0 to 2 use value at 1
2 to 4 use value at 3
4 to 6 use value at 5

f(1) = 1-2+2 = 1
f(3) = 9-6+2 = 5
f(5) = 25-10+2 = 17

so
2(1) + 2(5) + 2(17)