Math Problem Statement
Let f : [0, 4] → R be f(x) = x x ∈ [0, 2) 5 x = 2 2 x ∈ (2, 4] (a) Find a formula for F(x) = R x 1 f(t) dt. (b) What is F ′ (x)? Hint it is not f(x).
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Piecewise Functions
Integration
Differentiation
Formulas
F(x) = ∫_1^x f(t) dt
Derivative of F(x)
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Grades 11-12
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