a. Let a = x 0 < x 1 < x 2 < x
Question:
a. Let a = x0 < x1 < x2 · · · < xn = b be any partition of [a, b], and let F be any antiderivative of ƒ. Show that
b. Apply the Mean Value Theorem to each term to show that F(xi) - F(xi-1) = ƒ(ci)(xi - xi-1) for some ci in the interval (xi-1, xi). Then show that F(b) - F(a) is a Riemann sum for ƒ on [a, b].
c. From part (b) and the definition of the definite integral, show that
Transcribed Image Text:
F(b) - F(a) = n Σ [F(xi) - F(x-1)]. i=1
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ANSWER a We can write the lefthand side as Fb Fa Fxn Fxn1 Fxn1 Fxn2 Fx2 Fx1 Fx1 Fa Notice that each ...View the full answer
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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