the improper integral from 1 to + infinity
3e^(-x) - x^(4)
2x^(3) + x^(5)
A)diverges to + inf
B)exists and is finite
D)none of the preceding
The right answer is D but I can't see why.
Thank you for your help.
Regardless, look at the form of the integrand for large x (which translates in this case for any x greater than 5 - 10 or so.)
So compute .
This by itself is not an answer, but if you sketch the integrand over [1, 10] you will see that the area under the curve is clearly finite. Thus
Since this answer isn't listed, it must be answer D.
Firstly, thank you both. Then, I am getting a little bit confused..ok, now, I sketched the graph and clearly it shows the area is finite, but without that there are still some points that I don't get (sorry for annoying you.. ) I arrived 'till (-1/x), since qualitatively we can say the integrand will be like that, but then I am lost. As far as I remember, 1/x diverges and if something diverges then the area is infinite...which is surely not correct, otherwise the answer would have been another...help!
thanks thanks thanks so much