Question

You are given the function f(x) = 4 - x^2. Using four approximating rectangles and left endpoints, estimate the area under the graph of f(x) from x=0 to x=2. Estimated area = Repeat the above calculation using right endpoints. Estimated area = Your answers should have two digits after the decimal.

Answer #1

Estimate the area under the graph of f(x)=f(x)=3x^2+6x+7 over
the interval [0,5] using ten approximating rectangles and
right endpoints.
Repeat using left endpoints.

Estimate the area under the graph of f(x)=1/(x+2) over the
interval [0,3]using eight approximating rectangles and
right endpoints.
Rn=
Repeat the approximation using left endpoints.
Ln=

Estimate the area under the graph of f(x)=1/x from x=1
to x=2 using four approximating rectangles and left endpoints.

Estimate the area under the graph of f(x) = 4
cos(x) from x = 0 to x = π/2
using four approximating rectangles and right endpoints. (Round
your answers to four decimal places.)
Repeat with left endpoints.

Estimate the area under the graph of f(x)=1/(x+3) over the
interval [−2,1] using ten approximating rectangles and
right endpoints. a=-2,b=1,n=10
Rn=?
Repeat the approximation using left endpoints.
Ln?
Accurate to 4 places.

Estimate the area under the graph of f(x)=x2+4x from x=2 to x=10
using 4 approximating rectangles and left endpoints. Approximation
=

Estimate the area under the graph of
f(x)=1x+1f(x)=1x+1 over the interval [2,7][2,7] using eight
approximating rectangles and right endpoints.
Rn=Rn=
Repeat the approximation using left
endpoints.
Ln=Ln=
Round answers to 4
places. Remember not to round too early in your
calculations.

(a) Estimate the area under the graph of f(x) = 2/x from x = 1
to x = 2 using four approximating rectangles and right endpoints.
(Round your answer to four decimal places.)
(b) Repeat part (a) using left endpoints. (Round your answer to
four decimal places.)

Estimate the area under the graph of f(x)=x2+3x from x=1 to x=4
using 33 approximating rectangles and left endpoints.
Approximation =

30) Estimate the area under the graph of f(x)= 1/x+4 over the
interval [1,3] using five approximating rectangles and
right endpoints.
Rn=
Repeat the approximation using left endpoints.
Ln=

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