00:01
Hello, welcome to this lesson.
00:03
In this lesson, we'll use the reduction, the reduction formula to show that the integral sign to a sine squared x, the x is equal to x on 2 minus sign 2 x on 4 plus c.
00:40
Okay, let me add the c to it.
00:44
Probably the c comes after you have integrated this okay so we use this to show that so let's begin what we do is that we would identify the end then we plug it into this so here the end is 2 so it means that the integral sign squared dx sine square x x x is equal to 1 over 2 we are substituting into this go to cross x sign to the power n is 2 so n minus 1 x then plus 2 minus 1 on 2 then sign 2 minus 2 x d x okay so here it becomes half cost x sign x then plus 1 on 2 because the whole thing becomes zero and the whole of the sign is out of that so we have half cross x sign x plus half x squared okay, this is left with dx alone.
02:51
So that is the whole thing here is gone.
02:56
So it's left with dx.
02:59
So it becomes one on x, one on two x.
03:05
But from double angles we have sine 2a as cost a, sign a, sign a...