Calc
posted 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.

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
Respond to this Question
Similar Questions

Calculus
Estimate the area under the graph of f(x) = 2x^3 + 3 from x= 1 to x=5, first using 6 approximating rectangle and right endpoints, and then improving your estimate using 12 approximating rectangles and right endpoints. When using the … 
Calculus
Question Details: Do the following. (Round your answers to four decimal places.) (a) Estimate the area under the graph of f(x) = 8 + 2x2 from x = 1 to x = 2 using three rectangles and right endpoints. R3 = 1 Improve your estimate … 
Math: Calculus
Estimate the area under the graph of f(x)=3x^3+5 from x=1 to x=4, first using 5 approximating rectangles and right endpoints, and then improving your estimate using 10 approximating rectangles and right endpoints. I'm having problem … 
Math: Calculus
Estimate the area under the graph of f(x)=x^2+2x from x = 4 to x = 10 using 3 approximating rectangles and left endpoints. I got 290.25 as my answer but it's wrong. Would someone explain to me how to answer this question. 
CalculusApproximate areas
Estimate the area under the graph of f(x)= x^2 + 3 x from x=1 to x=10 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve at a) left endpoints: b) right endpoints: 
Calculus
a) Estimate the area under the graph of f(x)=7+4x^2 from x=1 to x=2 using three rectangles and right endpoints. R3= ? 
Calculus Help Please Urgent!!!
a) Estimate the area under the graph of f(x)=7+4x^2 from x=1 to x=2 using three rectangles and right endpoints. R3= ? 
Calc
Suppose that we want to estimate the area under the graph of f(x)=X^2+x for x=1 and 3. What is the value of the estimate using four rectangles and taking the sample points to be lefthand endpoints? 
Calculus
Estimate the area under the graph of f(x)= x^2 + 2 x from x=1 to x=5 using 4 approximating rectangles and left endpoints. 
calc
a) Estimate the area under the graph of f(x) = 10(sqrt(x)) from x = 0 to x = 4 using four approximating rectangles and right endpoints