Question

Calculate the trapezoidal sum for the function f ( x ) = x^ 2
over the interval [ 0 , 1 ] for n = 5 rectangles. **.34
Correct!!!!!!!**

f ( x ) = x^2 over the interval [ 0 , 1 ] Enter your answer as a whole number or a fraction. what the f*** is this asking for???????

Which of the three methods you used gave the best estimate to
the area under the curve for f ( x ) = x^2 on the interval [ 0 , 1
] ? **Trapezoid Rule Correct!!!!**

Answer #1

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.

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...

Estimate the area of the region bounded between the curve f(x) =
1 x+1 and the horizontal axis over the interval [1, 5] using a
right Riemann sum. Use n = 4 rectangles first, then repeat using n
= 8 rectangles. The exact area under the curve over [1, 5] is ln(3)
≈ 1.0986. Which of your estimates is closer to the true value?

For the function, do the following.
f(x) =
1
x
from a = 1 to b =
2.
(a) Approximate the area under the curve from
a to b by calculating a Riemann sum using 10
rectangles. Use the method described in Example 1 on page 351,
rounding to three decimal places.
square units
(b) Find the exact area under the curve from a to
b by evaluating an appropriate definite integral using the
Fundamental Theorem.
square units

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=

Approximate the area under f(x) = (x – 2, above the
x-axis, on [2,4] with n = 4 rectangles using the (a) left endpoint,
(b) right endpoint and (c) trapezoidal rule (i.e. the “average”
shortcut). Be sure to include endpoint values and write summation
notation for (a) and (b). Also, on (c), state whether the answer
over- or underestimates the exact area and why.

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.

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

unctions, each over the interval x = 0 to x = 6:
f(x) = x2 + 1
f(x) = 12 − 2x
f(x) = 36 − x2
f(x) = 2x + 1
Methods:
R: Right Riemann sum
Number of Rectangles: 1,
Create a report on the application you selected. Include the
problem statement (function, interval, method, number of
rectangles), mathematical and verbal work of finding the
approximate area under the curve, a graph of the
function/rectangles created at the Desmos...

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.

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