Math Problem Statement

Let g(x) = ∫₀ˣ f(t) dt, where f is the function whose graph is shown below. Evaluate g(x) for x = 0, 1, 2, 3, 4, 5, and 6. Also, estimate g(7) and determine at what value of x g attains its maximum.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Definite Integrals
Functions
Area under the Curve

Formulas

g(x) = ∫₀ˣ f(t) dt

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12 (AP Calculus level)

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