Question

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?

Answer 1

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.

Answer 2

That's probably close enough Damon. thanks!