Question

Calculate R4 right endpoint approximation for x^2 + x on the interval [0,2]

Answer 1

whats the width of our subintervals?

Answer 2

2 - 0 / 4 = 1/2?

Answer 3

1/2 is good for me

now the right end x values are:

2-.5 i : for i = 0,1,2,3 i beleive

Answer 4

is this a calculation done manually, or am I looking to use a limit formula?

Answer 5

for this question, its just a approximation using over or undersized areas of rectangles

Answer 6

meaning that I summate this by hand....calculate f(x) for n=i four times?

Answer 7

depends on the calulator you have but yeah it can be done by hand

\[\frac12\sum_{i=0}^{3}(2-i/2)^2+(2-i/2)\]

Answer 8

can it be done formulaicly or by any other means than summing the four f(x)'s?

Answer 9

i spose it can if you expand the ^2 and combine like terms .... then you have i^2 and i and a constant to formulate with

Answer 10

just guessing, but this is the beginning of integration for our calc class, and prof is likely wanting us to do it by hand....

Answer 11

prolly :)

x(1+x) might simplify the handiwork?

1/2 (2(3) + 1.5(2.5) + 1(2) + .5(1.5))

Answer 12

ok, thanks for the help

Answer 13

youre welcome