Asked by lmao
                determine whether the improper integral diverges or converges. evaluate if it converges. 
integral of e^-xcosxdx from 0 to infinity
i got the limit as b--> infinity for (-e^-xcosx + e^-xsinx) /2
Would I plug in my value for infinity and subtract it from the value I get when i plug in 0?
            
            
        integral of e^-xcosxdx from 0 to infinity
i got the limit as b--> infinity for (-e^-xcosx + e^-xsinx) /2
Would I plug in my value for infinity and subtract it from the value I get when i plug in 0?
Answers
                    Answered by
            oobleck
            
    that's the short way to do it.
Formally, you should take the limits, but since it is clear that e^-x goes to zero, it's pretty simple.
Even though cos(infinity) and sin(infinity) do not converge to a limit, we know that they are bounded by 1, so e^-x takes over.
    
Formally, you should take the limits, but since it is clear that e^-x goes to zero, it's pretty simple.
Even though cos(infinity) and sin(infinity) do not converge to a limit, we know that they are bounded by 1, so e^-x takes over.
                    Answered by
            lmao
            
    so what’s the answer? 1/2? 
And my way is still right , right ?
    
And my way is still right , right ?
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