A tricky integration problem. Save me

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SUMMARY

The integration problem discussed involves calculating the definite integral of the function exp(-x) cos(x) from 0 to infinity. The indefinite integral was correctly determined to be 0.5 exp(-x) [sin(x) - cos(x)]. The key insight is that as x approaches infinity, the term exp(-x) approaches zero, rendering the contributions of sin(x) and cos(x) negligible, confirming that the integral converges to a finite value.

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saksham
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I was asked to integrate( exp(-x) cos(x)) with respect to x with the limits x=0 and x= infinity.
I calculated the indefinite integral to be 0.5 exp(-x) [sin(x)-cos(x)].

I was stuck in the part where we apply limit x approaches infinity of sin(x) and cos x.

Please help me out.


Saksham
 
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e^-x goes to zero at infinity, so the other terms arent important, as long as theyre finite, which they clearly are.
 
Thanks for your reply StatusX. I really appreciate it.

Saksham
 

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