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 + 4 from x= -2 to x=2
Please show steps, thank you :)
f(x) -x^2 + 4 from x= -2 to x=2
Please show steps, thank you :)
Solution
If n = 4 and we\'re going from x = -2 to x = 2, then the intervals are [-2,-1],[-1,0],[0,1],[1,2] and the length of each interval is 1. a) f(-2) + f(-1) + f(0) + f(1) = (-(-2)^2 + 4) + (-(-1)^2 + 4) + (-(0)^2 + 4) + (-(1)^2 + 4) = (-4 + 4) + (-1 + 4) + 4 + (-1 + 4) = 0 + 3 + 4 + 3 = 10 b) f(-1) + f(0) + f(1) + f(2) = (-(-1)^2 + 4) + (-(0)^2 + 4) + (-(1)^2 + 4) + (-(2)^2 + 4) = (-1 + 4) + 4 + (-1 + 4) + (-4 + 4) = 3 + 4 + 3 +0 = 10 c) (10 + 10)/2 = 10 d) f(-1.5) + f(-.5) + f(.5) + f(1.5) = (-(-1.5)^2 + 4) + (-(-.5)^2 + 4) + (-(.5)^2 + 4) + (-(1.5)^2 + 4) = (-2.25 + 4) + (-.25 + 4) + (-.25 + 4) + (-2.25 + 4) = 1.75 + 3.75 + 3.75 + 1.75 = 11
