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 ]. 59. y = − 16 − x 2 ; y = 0 ; 0 ≤ x ≤ 4
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 ]. 59. y = − 16 − x 2 ; y = 0 ; 0 ≤ x ≤ 4
Solution Summary: The author calculates the area of the shaded region by using an online graphing calculator.
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].
59.
y
=
−
16
−
x
2
;
y
=
0
;
0
≤
x
≤
4
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.
8. Given, h(x) = 2 – x and g(x) = -x²+ 4
a) Plot the two functions on the same graph for -2 < x <4
b) Calculate the area between the curves of h(x) and g(x) for -2
7. If a side of an equilateral triangle has length x, express the area A of the triangle as a function of x.
A. A(x)= x?
В. А(х) — х?
C. A(x) = x?
D. A(x)=
Chapter 6 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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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