Question

I need help with this Area Under the Curve problem. The examples I was given aren't helping me and I want to understand this.

Answer 1

Well, what part of this doesn't make sense to you? The underlying concept of approximating the area under the curve with many rectangles, or the mechanics of actually evaluating it?

Answer 2

evaluating this problem specifically. Before, I was always given an equation, but now I have two y's and I don't know what to do with that

Answer 3

you have two problems here...

Answer 4

But which y goes with which x? I'm just unfamiliar with the way this was presented.

Answer 5

y=0 is the line of the x-axis. That's the bottom edge of the area.

y = sin x is the top edge of the area.

Answer 6

How so? in the graph, it shows the y= 1 as the top of the area

Answer 7

You're finding the area by finding the area of each of those rectangles. The top of the rectangle is the value of the curve at the midpoint of the rectangle. The bottom of the rectangle in this problem is the x-axis.

Answer 8

Yes, the highest the curve ever gets is y = 1, because the range of the sin function is from -1 to 1.

Answer 9

In the first problem, the height of the leftmost rectangle is about 3 1/2 boxes, where 5 boxes = 1. That makes it about 0.7. The width of the rectangle is 1 unit on the x axis, where 4 units = pi. That makes it pi/4 or about 0.785. So the area of the first box is 0.7*0.785 = 0.55, approximately. Now you repeat the process to find the area of the other boxes, and add them all up to approximate the area under the curve and above y = 0. Notice that in the first graph your boxes are laid out such that the 4th box has a height of 0, and quite a bit of space under the curve is left uncounted (although some space above the curve is also counted, which is equally undesirable).

Answer 10

Thank you so much for the explanation! :)