Posted by **Perry** on Wednesday, April 22, 2009 at 9:53pm.

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.

- Calc -
**Reiny**, Wednesday, April 22, 2009 at 10:26pm
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

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