In Problems 27–32, graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with double inequalities, and evaluate the indicated integral. 28. y = x 2 , y = x ; ∬ R 12 x y d A
In Problems 27–32, graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with double inequalities, and evaluate the indicated integral. 28. y = x 2 , y = x ; ∬ R 12 x y d A
Solution Summary: The author explains how to sketch the graph of the given equation and evaluate the iterated integral with the online graphing calculator.
In Problems 27–32, graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with double inequalities, and evaluate the indicated integral.
28.
y
=
x
2
,
y
=
x
;
∬
R
12
x
y
d
A
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
35. Find the maximum area of a rectangle inscribed in the region bounded by the graph of y = 4 − x and the axes (Figure 20).
1. Find the area of the region bounded by
y = -4x + 9, y = 2x² – 11x + 9, and the lines r = -2 and a = 5.
y =-4x + 9
|y = 2x² – 11x + 9
x = -2
x = 5
Chapter 7 Solutions
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY