Unformatted text preview: contains a polynomial expression that might allow you to use the fundamental identity sin 2 x + cos 2 x = 1 in one of three forms: cos 2 x = 1sin 2 x sec 2 x = 1 + tan 2 x tan 2 x = sec 2 x1 . If your function contains 1x 2 , as in the example above, try x = sin u ; if it contains 1+ x 2 try x = tan u ; and if it contains x 21, try x = sec u . Sometimes you will need to try something a bit diﬀerent to handle constants other than one. EXAMPLE 8.9 Evaluate Z p 49 x 2 dx . We start by rewriting this so that it looks more like the previous example: Z p 49 x 2 dx = Z p 4(1(3 x/ 2) 2 ) dx = Z 2 p 1(3 x/ 2) 2 dx....
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 Fall '07
 JonathanRogawski
 Math, Calculus, Trigonometry, Inverse function, Inverse trigonometric functions

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