Question

Find R5 and L5 for the area under the curve f(x) = x+1,
0<x<5, then find the exact area by finding the limit of
R_n

Answer #1

f(x) = 2x from a =
4 to b = 5
(a) Approximate the area under the curve from
a to b by calculating a Riemann sum using 5
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

f(x) = 1/x
from a = 1 to b =
3.
(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 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?

Find the area of the region under the curve
y =
e5x
from
x = 0
to
x = 3.

1. Find the area between the curve f(x)=sin^3(x)cos^2(x) and y=0
from 0 ≤ x ≤ π
2. Find the surface area of the function f(x)=x^3/6 + 1/2x from
1≤ x ≤ 2 when rotated about the x-axis.

1. Find the area of the region bounded by the graph of the
function f(x) = x4 − 2x2 + 8, the
x-axis, and the lines x = a and
x = b, where a < b and
a and b are the x-coordinates of the
relative maximum point and a relative minimum point of f,
respectively.
2.Evaluate the definite integral.
26
2
2x + 1
dx
0
3. Find the area of the region under the graph of f...

F(x)=4x-x^2
x= 0 to 2
two sub intervals
Approximate the area under the curve over the interval.

Approximate the area under the curve on the specified interval
as directed. f(x) = x · 10^x on [0, 4] with 4 subintervals of equal
width and midpoints for sample points?

Find the area under the curve ? = ? − ???(?), ? = 4(1 − ???(?))
for 0 ≤ t≤ π.

Use the definition to find an expression for the area under the
graph of f as a limit. Do not evaluate the limit.
f(x) = x2 +
1 + 2x
, 6 ≤ x ≤ 8
lim n → ∞
n
i = 1

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