Question

I'll medal. I need help with many questions. The first is: Use finite approximation to estimate the area under the graph of the given function on the stated interval as instructed. 1) f(x)=1/x between x=4 and x=8 using a upper sum with 2 rectangles of equal width.

Answer 1

First, please do all you can to get started:
1) sketch f(x)=(1/x) on the interval (0, 80
2) DRAW vertical limit lines at x=4 and x=8
3) Draw a vertical divider line at x=6
4) Determine the height of the two approximating rectanges; these rectangles will be larger than the exact areas they represent (that's what "upper sum" means).

The DRAW utility is available if you wish to use it to share your sketch.

Answer 2

i'm sketching on paper because i take my notebook with me to class and i need these as notes. i know you're supposed to create 2 intervals right? like from 4 to 6 and 6 to 8. i'm kinda confused on how to find the height though. i read somewhere that the 4 to 6 interval should have a height of 1? and im taking a guess when determining the height of the other to be 1/4? and then if thats correct, you multiply each of those by 2 and you find each area and add them together.

Answer 3

@mathmale

Answer 4

"i know you're supposed to create 2 intervals right? like from 4 to 6 and 6 to 8" YES

The function is y=(1/x). If x=4, y=(1/4). If x=6, y=(1/6). Finally, if x=8, y=(1/8).

Notice how we have 3 x values here and 3 y values. Too many, since we're working with only two approximating rectangles. I challenge you to determine WHICH 2 of these 3 values you should use for the heights of the rectangles.

Answer 5

i believe you use y=1/4 and y=1/6? my reasoning is that x=4 and x=6 are the beginning of each interval

Answer 6

You could draw rectangles under the curve of y=(1/x) or above the curve. That is the main question here. You are to use the "upper sum," meaning that you want your rectangles to extend from the x-axis to points ABOVE the curve.

Please draw your rectangles.