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Unformatted text preview: by a factor of 9 5 , so we make a correction and take F ( x ) = 5 9 x 9 5 to get F = f. 4 Then the fundamental theorem (in this case) gives Z 1 x 4 5 dx = [ F ( x )] 1 = F (1)F (0) = 5 9 . Note: The usual formula here is Z x n dx = 1 n + 1 x n +1 + c. Problem 5.5.1: Use the substitution u = 3 x to evaluate Z cos 3 x dx. Solution: With u = 3 x, we have du = 3 dx, or dx = du 3 . Substituting we get Z cos 3 x dx = Z cos u du 3 = 1 3 Z cos u du = 1 3 sin 3 x + c, where we have changed back to the original variables from the solution sin u + c using u = 3 x....
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 Summer '05
 Dodson
 Chain Rule, Derivative, Product Rule, Quotient Rule

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