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10 Integral-part3

# 10 Integral-part3 - Chapter 3(Integral Calculus 3.6 3.7 1...

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Chapter 3 积积 (Integral Calculus) 3.6 积积积积 3.7 积积积积积积 02/28/12 1

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3.6 积积积积积积积积积积积 improper integral 积积 (P175): + ∞ + ∞ = b a b a dx x f dx x f ) ( lim ) ( -∞ - = b a a b dx x f dx x f ) ( lim ) ( + ∞ + ∞ - -∞ + = b c b c a a dx x f dx x f dx x f ) ( lim ) ( lim ) ( 积积积积 : 积积积积积积 (convergent) 积积积积积 : 积积积积积积 (divergent) 02/28/12 2
Examples = + ∞ 1 2 x dx + ∞ b b x dx 1 2 lim b b x 1 1 lim - = + ∞ + - = + ∞ 1 1 lim b b 1 = = + ∞ 1 x dx ( 29 + 1 2 x + ∞ = 1 + ∞ x dx 1 1 1 = - + ∞ x = + ∞ 1 2 : x dx or divergent 积 02/28/12 3

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2 2 (1) (ln ) dx x x +∞ 2 (2) ln dx x x +∞ 1 (3) dx x +∞ (4) dx x +∞ -∞ 积积积积积积积积积积积积积积 2 1 1 1 1 lim lim ln ln ln2 ln2 b b b x b →+∞ →+∞ = - = - + = ÷ [ ] ( 29 2 lim ln | ln | lim ln(ln ) ln(ln2)

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