1-14 - ( a ) f ( u ) du. Example: Compare the areas of the...

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January 14, 2005 Today § 5.5 The substitution rule.
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The substitution rule If u = g ( x ) is a differentiable function whose range is an interval I and f is continuous on I , then Z f ( g ( x )) g 0 ( x ) dx = Z f ( u ) du.
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The substitution rule for definite inte- grals If u = g ( x ) is a differentiable function on [ a, b ] and f is continuous function on the range of g , then Z b a f ( g ( x )) g 0 ( x ) dx = Z g ( b ) g
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Unformatted text preview: ( a ) f ( u ) du. Example: Compare the areas of the fol-lowing 3 regions: • R 1 = { ( x, y ) : 0 ≤ x ≤ 1 , ≤ y ≤ 2 xe x } • R 2 = n ( x, y ) : 0 ≤ x ≤ 1 , ≤ y ≤ e √ x o • R 3 = ± ( x, y ) : 0 ≤ x ≤ π 2 , ≤ y ≤ e sin x sin 2 x ²...
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This note was uploaded on 03/09/2008 for the course CALC 1,2,3 taught by Professor Varies during the Spring '08 term at Lehigh University .

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1-14 - ( a ) f ( u ) du. Example: Compare the areas of the...

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