00:01
For this problem, we are asked to write a reman sum and then a definite integral representing the area of the region shown, and using the strip shown, and then we're asked to evaluate the integral exactly.
00:12
So we can see that, first of all, the area of each one of those strips, so i'll call it just a n here, would be equal to delta x, the width, times, well, we can write the height by figuring out a way to write this as y as a function of we can see that we have a drop of 3 over a run of 6.
00:36
So we can write that y equals x over 2 plus 3.
00:41
So we would have that we'd have delta x times x, let's say xn over 2 plus 3, where we have xn is the x value where we are along our triangle.
00:58
So in that case, we'd have that our last step here, delta x, would be equal to three, or excuse me, six divided by however many sub rectangles we have.
01:10
So we can write this then as x capital n over two plus three...