Estimate the area under f(x) = x^2 on [0,2] using right endpoint approximation given n = 4.

Answer 1

x = 0.5, 1, 1.5, 2

f(0.5) = 0.25

f(1) = 1

f(1.5) = 2.25

f(2 = 4

rectangle width = 1/2 = 0.5

sum of the areas is 0.5 * ( 0.25 + 1 + 2.25 + 4) = 0.5 * 7.5 = 3.75

the anti-derivative integral is (1/3)(X^3) , for x=[0,2]

the actual area is (1/3) ( 2^3 - 0 ^3) = 8/3 = 2 and 2/3