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Unformatted text preview: PART I LAYMAN’S STATEMENT g(x) = integral from a to b of f(x) where g’(x) = f(x). g(t) = ∫ x a dt t f ) ( Take the derivative of both sides: dx d g(t) = ∫ x a dt t f dx d ) ( Since integration and differentiation are inverse operations, they cancel each other out. g’(t) = f(t)dt So, g’(t) = f(t)dt and g(t) = ∫ x a dt t f ) ( , thus demonstrating the inverse relationship between integration and differentiation. This is the first part of the Fundamental Theorem of Calculus....
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