Asked by Perry
Estimate the area under the graph of f(x)= x^2 + 2 x from x=4 to x=10 using 3 approximating rectangles and left endpoints.
Answers
Answered by
Reiny
not clear what you mean by "left endpoints"
I would mark off x= 4,6,8, and 10
f(4), f(6), .. etc would give you the heights
Do you want the rectangles to overlap or underlap?
rectangle 1:
larger =2 x f(6) = 2(48) = 96
smaller = 2(f(4)) = 48
difference = 48, which cut in half is 24
so first rectangle estimation = 48+24 = 72
do the same for the other two
I got 128 and 200 for a total
estimation of 400
BTW, using integration gave me an exact area of 396
I would mark off x= 4,6,8, and 10
f(4), f(6), .. etc would give you the heights
Do you want the rectangles to overlap or underlap?
rectangle 1:
larger =2 x f(6) = 2(48) = 96
smaller = 2(f(4)) = 48
difference = 48, which cut in half is 24
so first rectangle estimation = 48+24 = 72
do the same for the other two
I got 128 and 200 for a total
estimation of 400
BTW, using integration gave me an exact area of 396
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