00:01
Hi, there is a question and this given if f is continuous on 0 to pi, use the substitution u equal to, okay, i'll be writing this afterwards, u equal to pi minus x to show that this equal to this.
00:14
So i have been given 0 to pi x f sin x dx.
00:22
If i use substitution u equal to pi minus x, so, from here du will be equal to minus dx and value of x will be equal to pi minus u.
00:35
And for limits when x is 0, these are the limits on x, x is 0, u will be equal to pi.
00:43
When x is pi, u will be equal to 0.
00:46
This comes out to be from, this is left hand side, from from pi to 0, x is pi minus u, f sine x, sine pi minus u, and minus du, dx will become minus du.
01:16
So, this is from 0 to, if i need to remove this negative sign, so limit will be interchanged 0 to pi, pi minus u, f, sin pi minus u is sin u, sin u du, okay.
01:44
So, this is i and this is also, this is equation number 1, this is equation number 2.
01:59
But we need to just see that if i write write u equal to x.
02:05
There will not be anything changed over here because i am just changing the name of u to x...