## anonymous one year ago How do you approach this one? equation coming ...

1. anonymous

Come up with a reasonably accurate estimate of $\int\limits_{1}^{\infty} \frac {e^{-x}}{ \sqrt{1+ x^{4}}} dx$

2. anonymous

Can you just say that 1/E^x will dominate?

3. ganeshie8

An estimation w/o knowing the amount of error is useless

4. dan815

you could expand e^-x to a few terms in taylor series

5. dan815

and state what the error is wrt to how many terms u expand upto

6. anonymous

Im not sure what you mean Dan..sorry.. If 1/E^x is dominant then the function is heading to 0 is there some way of just using the fundamental formula here? If I plot this function it seems to zero out by the time it hits 15, what if I integrate and then just do something like If f'[x] = Power[E, -x]/Sqrt[1 + x^4] Then the integration of f'[x] is f[15] - f[1]

7. anonymous

and I get 1.903373417798832 * 10^-8

8. dan815

|dw:1438279836414:dw|

9. dan815

|dw:1438279964137:dw|

10. dan815

u can use those other approximation methods u are doing there too

11. anonymous

Okay.. so I don't know if this will be correct but after concluding that the dominant term 1/E^x will approach zero, then examining the plot and seeing that the function approaches zero by about x=15, then taking the definite integral over several intervals of [1,15] [1,30] [1,100] , then I found to within 3 decimal places, the function converges upon 0.127