Question

Estimate the area under the graph of f left parenthesis x right parenthesis equals 5 x cubed f(x)=5x3 between x equals 0 x=0 and x equals 1 x=1 using each finite approximation below. a. A lower sum with two rectangles of equal width b. A lower sum with four rectangles of equal width c. An upper sum with two rectangles of equal width d. An upper sum with four rectangles of equal width

Answer #1

1) Use finite approximation to estimate the area under the graph
of f(x) = x^2 and above the graph of f(x) = 0 from Xo = 0 to Xn= 2
using
i) a lower sum with two rectangles of equal width
ii) a lower sum with four rectangles of equal width
iii) an upper sum with two rectangles of equal width
iv) an upper sum with four rectangles if equal width
2) Use finite approximation to estimate the area under...

Use finite approximation to estimate the area under the graph of
f(x)=x2 and above the graph of f(x)=0 from
x0=0 to xn =12 using
i) a lower sum with two rectangles of equal width.
ii) a lower sum with four rectangles of equal width.
iii) an upper sum with two rectangles of equal width.
iv) an upper sum with four rectangles of equal width.
The estimated area using a lower sum with two rectangles of
equal width is ______ square...

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.

(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

Estimate the area under the graph of f ( x ) = 1 x + 1 over the
interval [ 3 , 5 ] using two hundred approximating rectangles and
right endpoints
R n =
Repeat the approximation using left endpoints
L n =

For the function f(x) = x, estimate the area of the region
between the graph and the horizontal axis over the interval 0≤x≤4
using a .
a. Riemann Left Sum with eight left rectangles.
b. Riemann Right Sum with eight right rectangles.
c. A good estimate of the area.

(a) 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.)
R4 = 3.1631
Sketch the graph and the rectangles.
Is your estimate an underestimate or an overestimate?
underestimateoverestimate
(b) Repeat part (a) using left endpoints.
L4 = 4.7339
Sketch the graph and the rectangles.
Is your estimate an underestimate or an overestimate?
underestimateoverestimate

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.

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