Homework Sourseapproximate the area under the graph of fx and above the xax
approximate the area under the graph of f(x) and above the x-axis using the following methods with n=4 a) use left end points b) use right end points c) average the answers in parts a and b d) use midpoints. f(x)= x^2 from x=1 to x=5 Please help thank you :) Also, can you show steps? I\'m a little confused on how to solve.
Solution
a) left endpoints: just evaluate f at each endpoint and multiply by the interval:
Al = [f(1) + f(2) + f(3) + f(4)](b-a)/n = (1 + 4 + 9 + 16)(4/4) = 30
b) right endpoints: Ar = [f(2) + f(3) + f(4) + f(5)](4/4) = (4 + 9 + 16 + 25) = 54
c) A = (Al + Ar)/2 = (30+54)/2 = 42
d) A = [f(1.5) + f(2.5) + f(3.5) + f(4.5)](4/4) = (9/4 + 25/4 + 49/4 + 81/4) = 41
