CPM Homework Help : APCALC Problem 3-43

Write and evaluate a Riemann sum to estimate the area under the curve for $−1\le x\le1$ given $f(x) = x^4 − x^2$ . Choose the number of rectangles so that your answer will be a good approximation of the area. What is interesting about the sign of your result? Use a description or sketch of the function to support your answer.

Graph:

Continuous curve, coming from upper left, passing through (negative 1, comma 0), turning up at approximate point (negative 0.5, comma negative 0.5), turning down at the origin, turning up at approximate point (0.5, comma 0.5), passing through (1, comma 0), continuing up & right.

Answer:

Your answer should be relatively close to $\approx−0.26667$ . The answer is negative because the function is below the $x$ -axis on this interval.