00:01
So in this question, we're going to evaluate the remand sum for fx equals x squared on the closed interval from negative 1 to 1, with four subintervals determined in the following way.
00:14
So we're on the interval from negative 1 to 1, and x0, which is the left endpoint of my first subinterval, is negative 1.
00:26
This may not be perfectly the scale, but x1, the end point of that.
00:31
First sub -interval is negative a quarter.
00:35
X2, the end point of my second sub -interval is positive a quarter.
00:42
X3, which is the endpoint of my third sub -interval, is three -quarters, and x4, the right endpoint of the fourth sub -interval, is 1.
00:55
Now, as our sample points, x1 star, i am choosing negative three -quarter.
01:03
My x2 star that's 0 my x3 star that's 1 half and my x 4 star that's 7 8s and so what do i do i take the width of each of my sub intervals and i multiply by the value of the function at the indicated x i star and so for example this first sub -interval has a width of three -quarters, and i'm going to have to multiply that by the value of the function at the test point within that sub -interval, negative three -quarters...