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.
The difference between the true value of an integral and the value given by the trapezoidal rule or Simpson's rule is known as the error. In numerical analysis, the error is studied to determine how large n must be for
k
where k is a constant that
the error to be smaller than some specified amount. For both rules, the error is inversely proportional to a power of n, the number of subdivisions.. In other words, the error is roughly
depends on the function and the interval, andp is a power that depends only on the method used. With a little experimentation, you can find out what the power p is for the trapezoidal rule and for Simpson's rule.
Complete parts a. through c. below.
...
1
a. Find the exact value of
dx.
1
x* dx = (Type an integer or a decimal.)
Chapter 6 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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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