Asked by Alice
Find the area between the graph of f(x)= x(e^-x^2) and the x-axis for the interval (0, ∞). Your work must include the proper notation and show the antiderivative. If the integral diverges, show why.
Answers
Answered by
oobleck
∫xe^(-x^2) dx = -1/2 e^(-x^2)
so, integrating from 0 to ∞, that is
-1/2 [ lim(x->∞) e^(-x^2) - 1] = -1/2 [0 - 1] = 1/2
so, integrating from 0 to ∞, that is
-1/2 [ lim(x->∞) e^(-x^2) - 1] = -1/2 [0 - 1] = 1/2
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.