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1-121.

WHICH IS BETTER? Part Two

Below is a comparison between using rectangles and trapezoids to approximate the area under a curve for the same interval of a function. Decide which method you think will best approximate the area under the curve for . Then approximate the area using each method if , , and using sections. Compare your results with the actual area .

First quadrant graph, downward parabola, vertex in center of quadrant, with point at the origin, 3 equal width, vertical shaded bars, bottom edges on x axis, left edge of first bar labeled a, right edge of last bar labeled b, & with midpoint of top edge of each bar, on the parabola.

Midpoint Rectangles

First quadrant graph, downward parabola, vertex in center of quadrant, with point at the origin, 3 equal width vertical shaded trapezoids, bottom edges on x axis, left edge of first bar labeled a, right edge of last bar labeled b, & top right & left vertices of each bar is on the parabola, so each top edge is slanted, connecting consecutive x integer points on the parabola.

Trapezoids

Which method comes closer to the actual curve ?

Each section is units wide. Use this knowledge and the equation of the function to find the areas of each section for both methods.

Which method gave you the number closest to ?