0 like 0 dislike
0 like 0 dislike
If the improper integral from -infinity to infinity is 0 then there t0 such that the integral from t0 to infinity equal minus the integral from -infinity to t0

2 Answers

0 like 0 dislike
0 like 0 dislike
Look at it this way. T
If you split the area in two then you have  two areas that adds up to finite numbers. Let's call them L and R (left and right).


L+R = 0


So ..
0 like 0 dislike
0 like 0 dislike
> If the improper integral from -infinity to infinity is 0 then there t0 such that the integral from t0 to infinity equal minus the integral from -infinity to t0

If *f* is indeed integrable over **R** with (improper) integral 0, as is implicit in the statement of your exercise, then wouldn't it be the case that

- Integral\_-∞\^*t*\_0 *f*(*x*) d*x* = -Integral\_*t*\_0\^+∞ *f*(*x*) d*x*

for *every* *t*\_0 in **R**?

After all, when we take the equation

- Integral\_-∞\^+∞ *f*(*x*) d*x* = 0,

then decompose the domain (-∞,+∞) as the union (-∞,*t*\_0] ∪ [*t*\_0, +∞), what can we conclude?

Hope this helps point you in a useful direction. Good luck!

Related questions

0 like 0 dislike
0 like 0 dislike
0 answers
MorganHoover_ asked Jun 21
"Previous comparison of change in CAPS score between sertraline and placebo showed effect sizes of 0.31 and 0.37 (ref. 16). Similarly, comparison of change in CAPS score ...
MorganHoover_ asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
MSR_Tlse asked Jun 21
Are the S3/S4 Edexcel Further Maths units useful to become an actuary? Topics include sampling, unbiased and biased estimators, confidence intervals and significance test...
MSR_Tlse asked Jun 21
0 like 0 dislike
0 like 0 dislike
3 answers
Chiiild asked Jun 21
Received two job offers. I wish I would've taken the other job. Can I go back to the company I turned down?
Chiiild asked Jun 21
by Chiiild
0 like 0 dislike
0 like 0 dislike
6 answers
sigaouli asked Jun 21
Quitting job possibly to work on mental health issues but gap in employment could affect job prospects in the future
sigaouli asked Jun 21
0 like 0 dislike
0 like 0 dislike
2 answers
driveshift asked Jun 21
I did this all wrong but got the right answer? Took half of .075, used d=(1+i)/i to get discount rate, and just added. Decimal was off, but i got the numbers right. Luck?...
driveshift asked Jun 21

33.4k questions

135k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!