Use upper and lower sums to approximate the area under the curve using 7 sub intervals.

Question

The equation is y=sqrt(1-x²). The picture is a concave down curve that goes to 1 in both the y and x direction. I found the lower sum to be 0.6985 but I can not seem to get the uppper sum correct. 

Answer 1

Abigail,

 

I see no one answered this yet. If you are going from (0,1) to (1,0) then you have divided the x interval [0,1] into seven equal pieces and I assume you are approximating using rectangles not trapezoids.

 

The lower x values would be 0, 1/7, 2/7, 3/7, 4/7, 5/7 and 6/7.

 

The upper values would then be 1/7, 2/7, ..., 6/7, 1.

 

Whatever your calculations were for the lower approximation were, replace the one where you used x=0 with x=1 to get a different sum (approx.) which should be the upper approx.

 

 

Please let me know if I interpreted the question correctly and my solution works.

 

Arnold (again). I answered one of your other questions.