Question

Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule), estimate the area under the graph of the following function, using two and then four rectangles.

y=25-x^{2} between x=-5 and x=5

For two rectangles, area ≈______

For two rectangles, area ≈______

Answer #1

Using rectangles whose height is given by the value of the
function at the midpoint of the rectangle's base (the midpoint
rule), estimate the area under the graph of the following
function, using two and then four rectangles. y=4−x^2 between x =−
2 and x= 2

Using rectangles each of whose height is given by the value of
the function at the midpoint of the rectangle's base (the midpoint
rule), estimate the area under the graph of the following function,
using first two and then four rectangles. f(x)= 8/x between x =4
and x =8 Using two rectangles, the estimate for the area under the
curve is

Using rectangles whose height is given by the value of the
function at the midpoint of the rectangle's base, estimate the area
under the graph using first two and then four rectangles.
f(x)=x^(2) on [1,3], Using two rectangles to estimate, the area
under f(x) is approximately ,Using Four rectangles to estimate, the
area under f(x) is approximately

(1 bookmark) Use the midpoint rule to estimate the area under
graph of f(x) =5/x and above the graph of f(x) = 0 from X0 = 1 to
Xn =65 Using two rectangles equal width and four rectangles of
equal width

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.

Use the midpoint rule with 4 rectangles to approximate the area
under f(x)=x2 over [2,4]. Give your
answer as a fully simplified fraction.

Use finite approximations to estimate the area under the graph
of the function f(x) = 24−x2+2x between x = −4 and x = 6 for each
of the following cases. a. Using a lower sum with two rectangles of
equal width b. Using a lower sum with four rectangles of equal
width c. Using an upper sum with two rectangles of equal width d.
Using an upper sum with four rectangles of equal width

Use finite approximations to estimate the area under the graph
of the function f(x) =8−x2+2x between x = −2 and x = 4 for each of
the following cases. a. Using a lower sum with two rectangles of
equal width b. Using a lower sum with four rectangles of equal
width c. Using an upper sum with two rectangles of equal width d.
Using an upper sum with four rectangles of equal width

Use a finite approximation to estimate the area under the graph
of the given function on the stated interval as instructed. 1) f(x)
= x 2 between x = 3 and x = 7 using a left sum with four rectangles
of equal width.

Estimate the area under the curve described by
f(x)=x2+1
between [1, 3] using 8 rectangles. You may define the height of
your rectangles using the left- or right-edge.

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