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.
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
22. The tangent line to the graph of y= e–x at the point (3, 1) intersects the x-axis at the point P and the
y-axis at the point Q. What is the area of the triangle whose vertices are the origin, point P, and point
y%3D
Q?
(A) 2
(B) 4
(C) 8
(D) 16
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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