state the area between the lorenz curve L(x)=xe^(x-1) and the
x-axis as a definite integral. Approximate...
state the area between the lorenz curve L(x)=xe^(x-1) and the
x-axis as a definite integral. Approximate its value (to 3 decimal
places) using midpoints and n=5 equal with subintervals.
Approximate the area under f(x) = (x – 1)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.
1.
A Lorenz curve
measures the ___ on the vertical axis.
A)
cumulative percentage of families
B) demand
of families on welfare
C)
cumulative percentage of money income
D)
cumulative percentage of family wealth
2.
A Lorenz curve that is perfectly straight indicates
A) that a small portion of the population accounts for most of
the income.
B) that society is very rich.
C) that a large portion of the population accounts for most of
the income.
D) complete income...
What is the difference between and definite and indefinite
integral, the graphical interpretation of the definite integral and
the connection between the summation approximations. (left, right,
trapezoid) with the definite integral.
Approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with
n=4.
f(x)=88x+55
from
x=44
to
x=66
a.
Use left endpoints.
b.
Use right endpoints.
c.
Average the answers in parts a and b.
d.
Use midpoints.
Find the area between the curve and the x-axis over the
indicated interval.
y = 100 − x2;
[−10,10]
The area under the curve is ___
(Simplify your answer.)
Use Simpson’s Rule with n = 4 to approximate the value of the
definite integral ∫4 0 e^(−x^2) dx. (upper is 4, lower is 0)
Compute the following integrals (you may need to use Integration
by Substitution):
(a) ∫ 1 −1 (2xe^x^2) dx (upper is 1, lower is -1)
(b) ∫ (((x^2) − 1)((x^3) − 3x)^4)dx
approximate the area under f(x) = 10x - x2, above the
x-axis, on [1,7] with n = 6 rectangles using the left and right
endpoint, trapezoidal rule and midpoint methods (include summation
notation and endpoint values) and then find the exact area using a
definite integral (include a graph with shaded region)
Find the area between the curve and the x axis from [-1,5] .
f(x)=5x2-3x+4 .Use the Fundamental Theorem of
Calculus.
Find the Area using Right Hand Riemann Sums with n=10
Explain the difference between the two methods. Which of the two
methods is more accurate? How can you make the less accurate way
more accurate without changing the process?