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 ]. 61. y = − 4 − x 2 ; y = 4 − x 2 ; − 2 ≤ x ≤ 2
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 ]. 61. y = − 4 − x 2 ; y = 4 − x 2 ; − 2 ≤ x ≤ 2
Solution Summary: The author explains how the area bounded by the graphs of the equation y=-sqrt4-x2 is 12.566 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].
61.
y
=
−
4
−
x
2
;
y
=
4
−
x
2
;
−
2
≤
x
≤
2
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.
11) A cam is designed with a lens that is described as the following area
between two curves:
а+
+b.
Units are in cm.
The red top curve is f(x) = x3 - 2x2-x+2
The blue bottom curve is g(x) = x² - 1
Find the area in cm²
1. Find the total area bounded by the curves y = x² − 3x and y = x³ + x² − 12x.
1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and
shade the area
required.
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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