Let f(x) be odd and integral between -4 to 8 f(x)dx=1.

Integral Between 4 to 8 f(x)dx=?

Question

Let f(x) be odd and integral between -4 to 8 f(x)dx=1. 

Integral Between 4 to 8 f(x)dx=?

anonymous · Answer

second time i have seen this problem and i couldn't get it the first time
seems like it could be anything

anonymous · Answer

I know that there's a specific way to do it, but problem is i don't know how to apply it. xD

anonymous · Answer

ooh doh

anonymous · Answer

$$\int_{-4}^4f(x)dx=0$$ because the function is odd!!

anonymous · Answer

Apparently It's not the right answer. This is what I got a hint for.

anonymous · Answer

jeez sometimes i think my brain went on vacation

anonymous · Answer

yea so the part from -4 to 4 contributed nothing

anonymous · Answer

the part from 4 to 8 is one

anonymous · Answer

Sometimes I want to cry in a corner.

anonymous · Answer

lol me too

anonymous · Answer

$$\int_{-4}^8=\int_{-4}^4+\int_4^8=0+\int_4^8=1$$

anonymous · Answer

That seems right. lol actually yeah!

anonymous · Answer

oh yeah, it is right

anonymous · Answer

i would bet $\$87$ on it

anonymous · Answer

Hahaha Thanks :)

myininaya · Answer

And if f is odd then F is even so F(4)=F(-4)
$$\int\limits_{-4}^{8}f(x) dx=F(8)-F(-4)=F(8)-F(4)=1$$

myininaya · Answer

$$\text{ so } \int\limits_{4}^{8}f(x) dx=1 $$