8.8.32-eg - q-( x + 2) + lim b -2 + Z 1-2 dx x + 2 = lim a...

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Example Evaluate Z 1 - 4 dx q | x + 2 | . Since x + 2 0 when x ≥ - 2, it follows that | x + 2 | = x + 2 if x ≥ - 2 | x + 2 | = - ( x + 2) if x < - 2 . We remove the absolute value signs by splitting the integral into Z 1 - 4 dx q | x + 2 | = Z - 2 - 4 dx q - ( x + 2) + Z 1 - 2 dx x + 2 . Note that the function in the integrand is undefined at x = - 2 thus both integrals are improper. Therefore Z 1 - 4 dx q | x + 2 | = lim a →- 2 - Z a - 4 dx
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Unformatted text preview: q-( x + 2) + lim b -2 + Z 1-2 dx x + 2 = lim a -2--2 q-( x + 2) a-4 + lim b -2 + 2 x + 2 1 b = lim a -2--2 q-( a + 2) + 2 2 + lim b -2 + 2 3-2 b + 2 = 2 2 + 2 3 ....
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.

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