# 2Blecture5 - 2B Lecture 5 S e c ti o n 5.4 In d e fi n i te...

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2B - Lecture 5 Section 5.4 Indefinite integrals and The net change theorem.

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The fundamental theorem of calculus Suppose that F is differentiable and F’ is continuous over [a,b]. Then ’(x)dx = F(b)-F(a) =F(x)| a b a b definite integral
Suppose F is a differentiable function. Then = F(x) (a) Always (b) Sometimes (c) Never ’(x)dx 0 x Question

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Suppose F is a differentiable function. Then = F(x) (a) Always (b) Sometimes (c) Never ’(x)dx 0 x Question If F’ is continuous and F(0)=0
Read the following four statements, If f is continuous on the interval [a, b], set I= then: (i) I is the area bounded by the graph of f, the x-axis and the lines x = a and x = b (ii) I is a number (iii) I is an antiderivative of f(x) (iv) I may not exist Now choose the correct answer below. (a) (ii) only (b) (i) and (ii) only (c) (i) and (iii) only (d) (iv) only (x)dx a b Question

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Read the following four statements, If f is continuous on the interval [a, b], set I= then: (i) I is the area bounded by the graph of f, the x-axis and the lines x = a and x = b (ii) I is a number
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• Fall '09
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