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Home > PC > Chapter 2 > Lesson 2.3.5 > Problem 2-132

2-132.

You are trying to find the area for .

  1. Use rectangles to find the upper and lower bounds of the area.

    Upper Bound means that the rectangles will give an over estimate.

    Downward parabola, vertex at (0, comma 6), with 4 shaded bars each 1/4 unit wide, from 1 to 2, with left, top vertex on the curve, so that the right top corner of each bar is above the curve.

    Lower Bound means that the rectangles will give an under estimate.

    Downward parabola, vertex at (0, comma 6), with 4 shaded bars each 1/4 unit wide, from 1 to 2, with right, top vertex on the curve, so that the left top corner of each bar is below the curve.

  2. Express the sum of the lower bound using sigma notation.