Looks like it's simple but wierd integral

[YehiaMedhat]

What is it meant by substitution here? I have no idea about solving it

 

[topsquark]

View attachment 34649
What is it meant by substitution here? I have no idea about solving it

$\displaystyle \int_a^b f(-x) ~ dx$

Set y = -x. Now look at the limits of integration. The original lower limit is a, so the new lower limit will be -a. The original upper limit is b, so the new upper limit is -b. Thus
$\displaystyle \int_a^b f(-x) ~ dx = \int_{-a}^{-b} f(y) ~ d(-y)$

What does this simplify to?

-Dan

 

[YehiaMedhat]

Well, so the negative will flip the limits, won't it?!!

 

[topsquark]

Well, so the negative will flip the limits, won't it?!!

Yes.

-Dan

 

[YehiaMedhat]

Thanks?