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.
In Problems 85–90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zerocorrect to two decimal places.
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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