2Blecture5 - 2B - Lecture 5 Section 5.4 Indefinite...

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Unformatted text preview: 2B - Lecture 5 Section 5.4 Indefinite integrals and The net change theorem. 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 x Question Suppose F is a differentiable function. Then = F(x) (a) Always (b) Sometimes (c) Never ́' ’(x)dx 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 ́G (x)dx a b Question 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...
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This note was uploaded on 12/07/2010 for the course MATH MATH 2B taught by Professor Famiglietti,c during the Fall '09 term at UC Irvine.

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2Blecture5 - 2B - Lecture 5 Section 5.4 Indefinite...

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