Math Problem Statement

Approximate the area under the following curve and above the x-axis on the given interval, using rectangles whose height is the value of the function at the left side of the rectangle. (a) Use two rectangles. (b) Use four rectangles. (c) Use a graphing calculator (or other technology) and 40 rectangles.

f(x)= 5+x2; [- 2,2]

...

(a) The approximated area when using two rectangles is 28 square units. (Type an integer or decimal rounded to two decimal places as needed.)

(b) The approximated area when using four rectangles is 26 square units. (Type an integer or decimal rounded to two decimal places as needed.)

(c) The approximated area when using 40 rectangles is (Type an integer or decimal rounded to two decimal places as needed.)

square units.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Riemann Sum
Area Approximation

Formulas

Left Riemann Sum Formula: A ≈ Σ [f(x_i) * Δx]

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12