5.3

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5.3 The Fundamental Theorem of Calculus
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Examples
Use WolframAlpha to determine g. Then determine
g'(x).
Question So what does g represent here?
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First Fundamental Theorem of Calculus Part 1
If f is continuous on a, b, then the function g
is defined by
is continuous on a, b and differentiable on
(a, b), then g(x) is the _______________ of f(t)
in terms of x. That is, g'(x) _____.
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First Fundamental Theorem of Calculus Part 1
(Alternate Definition)
If f is continuous on a, b, then
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Examples
Evaluate the following.
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Examples
Use WolframAlpha to determine the following
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First Fundamental Theorem of Calculus Part 1
(Alternate Definition)
If f is continuous on a, b and u is a function
of x, then
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Examples
Determine the derivative of g by hand.
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First Fundamental Theorem of Calculus Part 2
If f is continuous on a, b, then the function g
is defined by
where F is the general antiderivative of f, that
is, a function such that F ' f.
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Examples
Evaluate