CALC
1-14

1-14 - Today 5.5 The substitution rule The substitution...

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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 f ( g ( x )) g ( x ) dx = f ( u ) du.
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 b a f ( g ( x )) g ( x ) dx

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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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