r****y
发帖数: 1437 | 1 let f(x) = exp(-1/x^2)
integrate f(x) from 0 to +inf, what we would get?
Maple gives me a -sqrt(\pi), but this integral could not be negative.
Anyone sheds light on it? |
H****h
发帖数: 1037 | 2 先换元。
negative.
【在 r****y 的大作中提到】
: let f(x) = exp(-1/x^2)
: integrate f(x) from 0 to +inf, what we would get?
: Maple gives me a -sqrt(\pi), but this integral could not be negative.
: Anyone sheds light on it?
|
r****y
发帖数: 1437 | 3 If you draw a plot of x vs. exp(-1/x^2), the area underneath
is negative?
【在 H****h 的大作中提到】
: 先换元。
:
: negative.
|
H****h
发帖数: 1037 | 4 let y=1/x. then integrate by part.
【在 r****y 的大作中提到】
: If you draw a plot of x vs. exp(-1/x^2), the area underneath
: is negative?
:
|
r****y
发帖数: 1437 | 5 Both exp(-1/x^2) and 1-exp(-1/x^2) has a value for int from 0 to
inf ba? Then add them up, no integral ah.
My mind is not right at a late time like now... :-(
【在 H****h 的大作中提到】
: let y=1/x. then integrate by part.
|
H****h
发帖数: 1037 | 6 等会儿。
【在 r****y 的大作中提到】
: Both exp(-1/x^2) and 1-exp(-1/x^2) has a value for int from 0 to
: inf ba? Then add them up, no integral ah.
: My mind is not right at a late time like now... :-(
|
i*****u
发帖数: 26 | 7 x --> +inf 时f(x)难道不是--> 1 吗？这样的话积分发散。
negative.
【在 r****y 的大作中提到】
: Both exp(-1/x^2) and 1-exp(-1/x^2) has a value for int from 0 to
: inf ba? Then add them up, no integral ah.
: My mind is not right at a late time like now... :-(
|
r****y
发帖数: 1437 | 8 ft. you are so right. 越老越糊涂了。
【在 i*****u 的大作中提到】
: x --> +inf 时f(x)难道不是--> 1 吗？这样的话积分发散。
:
: negative.
|
H****h
发帖数: 1037 | 9 1-f是可以从0到无穷积分的，但我不会算这个积分。
【在 r****y 的大作中提到】
: ft. you are so right. 越老越糊涂了。
|
n*******l
发帖数: 2911 | 10 As you said, change variable y=1/x and integrate by parts.
And the result is something like sqrt(pi) or a multiple of it.
【在 H****h 的大作中提到】
: 1-f是可以从0到无穷积分的，但我不会算这个积分。
|
H****h
发帖数: 1037 | 11 对
【在 n*******l 的大作中提到】
: As you said, change variable y=1/x and integrate by parts.
: And the result is something like sqrt(pi) or a multiple of it.
|
