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.
4. A box with an open top is to be constructed from a rectangular piece of cardboard
with dimensions 14 cm by 22 cm by cutting out equal squares of side x at each
corner and then folding up the sides as shown in Figure 3. Express the volume V
of the box as a function of x.
- 22-
Figure 3
8
et
dt
7t
21.
sin(9x)
1.
16 + x<
X
dx
Chapter 6 Solutions
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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