Calculus
posted by mathstudent .
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 TI89 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 TI89 calculator return the wrong answer of 1? I assume the text book devised this problem to exploit some computer weakness?

Perhaps the calculator is doing a numerical integration and the components are going ++++ with the phase of the cosine and it is just asking too much of the poor little calculator :)
In other words, I have no idea. 
That's probably close enough Damon. thanks!
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