do solve it

If f(x)is be periodic with period λ & f(-x)+f(x) =0

Prove that ax∫f(t)dt is periodic with λ

27 Answers

33
Abhishek Priyam ·

graph se to thik hai.. par thinking of algebraic....(i am working on weak points.. :P)

let F(x)=a∫xf(t)dt
F(x+λ)=a∫x+λf(t)dt
F(x+λ)=a∫xf(t)dt+x∫x+λf(t)dt
F(x+λ)=F(x)+x∫x+λf(t)dt

iske aage.. ??

62
Lokesh Verma ·

priyam you can still do it algebraically!

It is very simple!

33
Abhishek Priyam ·

phew!!

The point was i wanted to solve this one widout any visualisataion of question... [3]

1
Philip Calvert ·

[1]

62
Lokesh Verma ·

Good work philip..

I din wnat to give away everything isliye gave only this much away to priyam ;)

1
Philip Calvert ·

arre kya zarurat hai algebraic se karne ki
put
t= k + x + lamba /2

dt = dk

limits now bcome -λ/2 to λ/2 (hopefully [3])

and that is zero............... i wonder if u want to do that also algebraically (but even then its doable)

33
Abhishek Priyam ·

graph se to dikh hi raha hai.. ki x to x+λ zero hoga... but i haev decided to do it algebraiclly....... k=t-x acha dekhte hain...

62
Lokesh Verma ·

priyam

in that integral you gave substitute k=t-x

11
Mani Pal Singh ·

HINT
ITS AN ODD FUNCTION!!!!!!!!!!!!!!

62
Lokesh Verma ·

hence it also shows that integral from c to λ+c will be zero?

33
Abhishek Priyam ·

x∫x+λf(t)dt=0 ana chahiye.... [12]par kaise..

33
Abhishek Priyam ·

-x se x tak zero.. hoga... lekin isse kya fayda...uske aage karne ke liye..

11
Mani Pal Singh ·

iske aage hi to nikaalna hai
good beginning but do end it with a good end[1]

62
Lokesh Verma ·

Hint: what will integral from -λ/2 to λ/2 be /???

1
vector ·

is ur q cmplete

11
Mani Pal Singh ·

i didnt thought that way
i will be glad to see some justification(theoretical or graphical)[1]

62
Lokesh Verma ·

No it is not useless.. but now it should ring a bell in all your heads..

That is because if you can think of a graph .. lot of areas get cancelled to zero :P

11
Mani Pal Singh ·

sir we have to prove the obvious thing[1]

SIR IF U THINK THIS QUESTION IS USELESS THEN WE MAY LEAVE THIS QUESTION!!!!!!!!!!!

62
Lokesh Verma ·

yes abhi..

yes mani now this question is obvious ;)

11
Mani Pal Singh ·

it was not mentioned in the question.............
that wont effect the ques
but abhi u should understand the motive of the ques!!!!!!!!!!!

13
Двҥїяuρ now in medical c ·

wat is 'a' there...any constant???

11
Mani Pal Singh ·

SORRY GUYZ AND GALS
BUT BHOOK LAG RAHI THI [3]
I HOPE ITS COMPLETE NOW

NOW ITS CORECTED

62
Lokesh Verma ·

manipal you are trying to say that f(x)+f(-x)=0?

11
Mani Pal Singh ·

that should have been understood
not a big matter it was
now focus.............

i hope its clear now!!!!!!!!!!!!!!!!!!!!

33
Abhishek Priyam ·

q samajh me nahi aya :P [7]

13
deepanshu001 agarwal ·

the 1st statement itself doest mak sense
kya angrezi likhi hai

11
Mani Pal Singh ·

perfectly complete
its a question worth spending time upon

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