Use FTC II from single-variable calculus to prove the second part of the Fundamental Theorem of Calculus
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Use FTC II from single-variable calculus to prove the second part of the Fundamental Theorem of Calculus for Vector-Valued Functions.
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Fundamental Theorem of Calculus for Vector-Valued Functions Part I: If r(t) is continuous on [a, b], and R(1) is an antiderivative of r(t), then S." r(t) dt = R(b) - R(a) Part II: Assume that r(t) is continuous on an open interval I and let a be in I. Then d dt r(s) ds = r(t)
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