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October 31, 2014

October 31, 2014

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

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?

- Calculus -
**Damon**, Sunday, January 13, 2008 at 3:56pmPerhaps 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.

- Calculus -
**mathstudent**, Sunday, January 13, 2008 at 4:28pmThat's probably close enough Damon. thanks!

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