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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

The Second Fundamental Theorem of Calculus Exercises

Example 1

Let f(x) = sin x and a = 0. Define

Find each value and represent using a graph of sin t.

(a) F(-π)

(b) F(2π)

(c) 

(d) Consider all real values of x. For what values of x is F(x)

(i) positive?

(ii) negative?

(iii) zero?

Example 2

Let

Find each value and represent each value using a graph of the function (1 – t).

(a) F(3)

(b) F(1)

(c) F(0)

(d) F(-1)

(e) F(-2)

Example 3

Use the second FTC to build two different antiderivatives of the function f(x) = eex.

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