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August 3, 2015

Homework Help: Calculus

Posted by mathstudent on Sunday, January 13, 2008 at 3:34pm.

My book says to do the following problem via computer and via hand:

Calculate the definite Integral of
e^-x * cos x dx
over (0, +infinity)

My TI-89 calculator gets 1 (it gets the same thing when I replace infinity with 999).

when I do this by hand, I get: 1/2.

The formula e^-x * cos x dx integrates to:
1/2 * e^-x * (sin x - cos x)

calculating:
limit b->infinity: 1/2 * e^-b * (sin b - cos b) - 1/2 * e^0 * (sin 0 - cos 0)
= 0 - 1 * (0 - 1/2) = 1/2

1/2 matches the book's answer. My question is why does my TI-89 calculator return the wrong answer of 1? I assume the text book devised this problem to exploit some computer weakness?

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