In Problems 57 – 62 , set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval . Find the areas to three decimal places . [Hint: A circle of radius r , with center at the origin , has equation x 2 + y 2 = r 2 and area π r 2 ]. 62. y = − 100 − x 2 ; y = 100 − x 2 ; − 10 ≤ x ≤ 10
In Problems 57 – 62 , set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval . Find the areas to three decimal places . [Hint: A circle of radius r , with center at the origin , has equation x 2 + y 2 = r 2 and area π r 2 ]. 62. y = − 100 − x 2 ; y = 100 − x 2 ; − 10 ≤ x ≤ 10
Solution Summary: The author explains how the area bounded by the graphs of the equation is 314.159 square unit.
In Problems 57–62, set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. [Hint: A circle of radius r, with center at the origin, has equation x2 + y2 = r2 and area πr2].
62.
y
=
−
100
−
x
2
;
y
=
100
−
x
2
;
−
10
≤
x
≤
10
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
3. To the right is a plot of the line of equality and the Lorenz curve
Lorenz Curve - Poland 2018
for Poland in the year 2018. Shade the area we need to find first
so that we can calculate the Gini index. Then, write an expression
for THIS AREA that includes a definite integral.
y = 2.0833x5 -3.75x4 + 2.2708x³
+0.1125x² +0.2833x
-Poland
-Line of Equality
0
1
0.2
0.4
0.6
0.8
Cumulative Percentage of the Population
4. Use the integral expression you wrote in #3 and the Fundamental Theorem of Calculus to find the Gini index
for Poland in the year 2018. Show the substitutions necessary, but use fnint to do the calculation.
5.
Which country has more income EQUALITY? Explain how you know.
Cumulative Wealth
1
0.8
0.6
0.4
0.2
0
Chapter 6 Solutions
Additional Calculus Topics for Calculus for Business, Economics, Life Sciences and Social Sciences
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Numerical Integration Introduction l Trapezoidal Rule Simpson's 1/3 Rule l Simpson's 3/8 l GATE 2021; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=zadUB3NwFtQ;License: Standard YouTube License, CC-BY