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.
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apclassroom.collegeboard.org
2. The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that
they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number
of bacteria present is given by
f(t)=5000.1
Under certain storage conditions, where t is time in days after packing of the product and the value of f(t) is in
millions.
The solution to word problems should always be given in a complete sentence, with appropriate units, in the
context of the problem.
(a) If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take?
(b) If t=0 corresponds to January 1, what date should be placed on the product?
2.6 Applications: Growth and Decay; Mathematics of Finances
1. A couple wants to have $50,000 in 5 years for a down payment on a new house.
(a) How much should they deposit today, at 6.2% compounded quarterly, to have the required amount in 5
years?
(b) How much interest will be earned?
(c) If they can deposit only $30,000 now, how much more will they need to complete the $50,000
after 5 years? Note, this is not 50,000-P3.
Chapter 6 Solutions
Calculus for Business Economics Life Sciences and Social Sciences Plus NEW
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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