Calculus
Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
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Chapter 4.4, Problem 52PS
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To sketch: The graph of the given function.

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Chapter 4 Solutions

Calculus

Ch. 4.1 - Prob. 1PSCh. 4.1 - Prob. 2PSCh. 4.1 - Prob. 3PSCh. 4.1 - Prob. 4PSCh. 4.1 - Prob. 5PSCh. 4.1 - Prob. 6PSCh. 4.1 - Prob. 7PSCh. 4.1 - Prob. 8PSCh. 4.1 - Prob. 9PSCh. 4.1 - Prob. 10PS
Ch. 4.1 - Prob. 11PSCh. 4.1 - Prob. 12PSCh. 4.1 - Prob. 13PSCh. 4.1 - Prob. 14PSCh. 4.1 - Prob. 15PSCh. 4.1 - Prob. 16PSCh. 4.1 - Prob. 17PSCh. 4.1 - Prob. 18PSCh. 4.1 - Prob. 19PSCh. 4.1 - Prob. 20PSCh. 4.1 - Prob. 21PSCh. 4.1 - Prob. 22PSCh. 4.1 - Prob. 23PSCh. 4.1 - Prob. 24PSCh. 4.1 - Prob. 25PSCh. 4.1 - Prob. 26PSCh. 4.1 - Prob. 27PSCh. 4.1 - Prob. 28PSCh. 4.1 - Prob. 29PSCh. 4.1 - Prob. 30PSCh. 4.1 - Prob. 31PSCh. 4.1 - Prob. 32PSCh. 4.1 - Prob. 33PSCh. 4.1 - Prob. 34PSCh. 4.1 - Prob. 35PSCh. 4.1 - Prob. 36PSCh. 4.1 - Prob. 37PSCh. 4.1 - Prob. 38PSCh. 4.1 - Prob. 39PSCh. 4.1 - Prob. 40PSCh. 4.1 - Prob. 41PSCh. 4.1 - Prob. 42PSCh. 4.1 - Prob. 43PSCh. 4.1 - Prob. 44PSCh. 4.1 - Prob. 45PSCh. 4.1 - Prob. 46PSCh. 4.1 - Prob. 47PSCh. 4.1 - Prob. 48PSCh. 4.1 - Prob. 49PSCh. 4.1 - Prob. 50PSCh. 4.1 - Prob. 51PSCh. 4.1 - Prob. 52PSCh. 4.1 - Prob. 53PSCh. 4.1 - Prob. 54PSCh. 4.1 - Prob. 55PSCh. 4.1 - Prob. 56PSCh. 4.1 - Prob. 57PSCh. 4.1 - Prob. 58PSCh. 4.1 - Prob. 59PSCh. 4.1 - Prob. 60PSCh. 4.2 - Prob. 1PSCh. 4.2 - Prob. 2PSCh. 4.2 - Prob. 3PSCh. 4.2 - Prob. 4PSCh. 4.2 - Prob. 5PSCh. 4.2 - Prob. 6PSCh. 4.2 - Prob. 7PSCh. 4.2 - Prob. 8PSCh. 4.2 - Prob. 9PSCh. 4.2 - Prob. 10PSCh. 4.2 - Prob. 11PSCh. 4.2 - Prob. 12PSCh. 4.2 - Prob. 13PSCh. 4.2 - Prob. 14PSCh. 4.2 - Prob. 15PSCh. 4.2 - Prob. 16PSCh. 4.2 - Prob. 17PSCh. 4.2 - Prob. 18PSCh. 4.2 - Prob. 19PSCh. 4.2 - Prob. 20PSCh. 4.2 - Prob. 21PSCh. 4.2 - Prob. 22PSCh. 4.2 - Prob. 23PSCh. 4.2 - Prob. 24PSCh. 4.2 - Prob. 25PSCh. 4.2 - Prob. 26PSCh. 4.2 - Prob. 27PSCh. 4.2 - Prob. 28PSCh. 4.2 - Prob. 29PSCh. 4.2 - Prob. 30PSCh. 4.2 - Prob. 31PSCh. 4.2 - Prob. 32PSCh. 4.2 - Prob. 33PSCh. 4.2 - Prob. 34PSCh. 4.2 - Prob. 35PSCh. 4.2 - Prob. 36PSCh. 4.2 - Prob. 37PSCh. 4.2 - Prob. 38PSCh. 4.2 - Prob. 39PSCh. 4.2 - Prob. 40PSCh. 4.2 - Prob. 41PSCh. 4.2 - Prob. 42PSCh. 4.2 - Prob. 43PSCh. 4.2 - Prob. 44PSCh. 4.2 - Prob. 45PSCh. 4.2 - Prob. 46PSCh. 4.2 - Prob. 47PSCh. 4.2 - Prob. 48PSCh. 4.2 - Prob. 49PSCh. 4.2 - Prob. 50PSCh. 4.2 - Prob. 51PSCh. 4.2 - Prob. 52PSCh. 4.2 - Prob. 53PSCh. 4.2 - Prob. 54PSCh. 4.2 - Prob. 55PSCh. 4.2 - Prob. 56PSCh. 4.2 - Prob. 57PSCh. 4.2 - Prob. 58PSCh. 4.2 - Prob. 59PSCh. 4.2 - Prob. 60PSCh. 4.3 - Prob. 1PSCh. 4.3 - Prob. 2PSCh. 4.3 - Prob. 3PSCh. 4.3 - Prob. 4PSCh. 4.3 - Prob. 5PSCh. 4.3 - Prob. 6PSCh. 4.3 - Prob. 7PSCh. 4.3 - Prob. 8PSCh. 4.3 - Prob. 9PSCh. 4.3 - Prob. 10PSCh. 4.3 - Prob. 11PSCh. 4.3 - Prob. 12PSCh. 4.3 - Prob. 13PSCh. 4.3 - Prob. 14PSCh. 4.3 - Prob. 15PSCh. 4.3 - Prob. 16PSCh. 4.3 - Prob. 17PSCh. 4.3 - Prob. 18PSCh. 4.3 - Prob. 19PSCh. 4.3 - Prob. 20PSCh. 4.3 - Prob. 21PSCh. 4.3 - Prob. 22PSCh. 4.3 - Prob. 23PSCh. 4.3 - Prob. 24PSCh. 4.3 - Prob. 25PSCh. 4.3 - Prob. 26PSCh. 4.3 - Prob. 27PSCh. 4.3 - Prob. 28PSCh. 4.3 - Prob. 29PSCh. 4.3 - Prob. 30PSCh. 4.3 - Prob. 31PSCh. 4.3 - Prob. 32PSCh. 4.3 - Prob. 33PSCh. 4.3 - Prob. 34PSCh. 4.3 - Prob. 35PSCh. 4.3 - Prob. 36PSCh. 4.3 - Prob. 37PSCh. 4.3 - Prob. 38PSCh. 4.3 - Prob. 39PSCh. 4.3 - Prob. 40PSCh. 4.3 - Prob. 41PSCh. 4.3 - Prob. 42PSCh. 4.3 - Prob. 43PSCh. 4.3 - Prob. 44PSCh. 4.3 - Prob. 45PSCh. 4.3 - Prob. 46PSCh. 4.3 - Prob. 47PSCh. 4.3 - Prob. 48PSCh. 4.3 - Prob. 49PSCh. 4.3 - Prob. 50PSCh. 4.3 - Prob. 51PSCh. 4.3 - Prob. 52PSCh. 4.3 - Prob. 53PSCh. 4.3 - Prob. 54PSCh. 4.3 - Prob. 55PSCh. 4.3 - Prob. 56PSCh. 4.3 - Prob. 57PSCh. 4.3 - Prob. 58PSCh. 4.3 - Prob. 59PSCh. 4.3 - Prob. 60PSCh. 4.4 - Prob. 1PSCh. 4.4 - Prob. 2PSCh. 4.4 - Prob. 3PSCh. 4.4 - Prob. 4PSCh. 4.4 - Prob. 5PSCh. 4.4 - Prob. 6PSCh. 4.4 - Prob. 7PSCh. 4.4 - Prob. 8PSCh. 4.4 - Prob. 9PSCh. 4.4 - Prob. 10PSCh. 4.4 - Prob. 11PSCh. 4.4 - Prob. 12PSCh. 4.4 - Prob. 13PSCh. 4.4 - Prob. 14PSCh. 4.4 - Prob. 15PSCh. 4.4 - Prob. 16PSCh. 4.4 - Prob. 17PSCh. 4.4 - Prob. 18PSCh. 4.4 - Prob. 19PSCh. 4.4 - Prob. 20PSCh. 4.4 - Prob. 21PSCh. 4.4 - Prob. 22PSCh. 4.4 - Prob. 23PSCh. 4.4 - Prob. 24PSCh. 4.4 - Prob. 25PSCh. 4.4 - Prob. 26PSCh. 4.4 - Prob. 27PSCh. 4.4 - Prob. 28PSCh. 4.4 - Prob. 29PSCh. 4.4 - Prob. 30PSCh. 4.4 - Prob. 31PSCh. 4.4 - Prob. 32PSCh. 4.4 - Prob. 33PSCh. 4.4 - Prob. 34PSCh. 4.4 - Prob. 35PSCh. 4.4 - Prob. 36PSCh. 4.4 - Prob. 37PSCh. 4.4 - Prob. 38PSCh. 4.4 - Prob. 39PSCh. 4.4 - Prob. 40PSCh. 4.4 - Prob. 41PSCh. 4.4 - Prob. 42PSCh. 4.4 - Prob. 43PSCh. 4.4 - Prob. 44PSCh. 4.4 - Prob. 45PSCh. 4.4 - Prob. 46PSCh. 4.4 - Prob. 47PSCh. 4.4 - Prob. 48PSCh. 4.4 - Prob. 49PSCh. 4.4 - Prob. 50PSCh. 4.4 - Prob. 51PSCh. 4.4 - Prob. 52PSCh. 4.4 - Prob. 53PSCh. 4.4 - Prob. 54PSCh. 4.4 - Prob. 55PSCh. 4.4 - Prob. 56PSCh. 4.4 - Prob. 57PSCh. 4.4 - Prob. 58PSCh. 4.4 - Prob. 59PSCh. 4.4 - Prob. 60PSCh. 4.5 - Prob. 1PSCh. 4.5 - Prob. 2PSCh. 4.5 - Prob. 3PSCh. 4.5 - Prob. 4PSCh. 4.5 - Prob. 5PSCh. 4.5 - Prob. 6PSCh. 4.5 - Prob. 7PSCh. 4.5 - Prob. 8PSCh. 4.5 - Prob. 9PSCh. 4.5 - Prob. 10PSCh. 4.5 - Prob. 11PSCh. 4.5 - Prob. 12PSCh. 4.5 - Prob. 13PSCh. 4.5 - Prob. 14PSCh. 4.5 - Prob. 15PSCh. 4.5 - Prob. 16PSCh. 4.5 - Prob. 17PSCh. 4.5 - Prob. 18PSCh. 4.5 - Prob. 19PSCh. 4.5 - Prob. 20PSCh. 4.5 - Prob. 21PSCh. 4.5 - Prob. 22PSCh. 4.5 - Prob. 23PSCh. 4.5 - Prob. 24PSCh. 4.5 - Prob. 25PSCh. 4.5 - Prob. 26PSCh. 4.5 - Prob. 27PSCh. 4.5 - Prob. 28PSCh. 4.5 - Prob. 29PSCh. 4.5 - Prob. 30PSCh. 4.5 - Prob. 31PSCh. 4.5 - Prob. 32PSCh. 4.5 - Prob. 33PSCh. 4.5 - Prob. 34PSCh. 4.5 - Prob. 35PSCh. 4.5 - Prob. 36PSCh. 4.5 - Prob. 37PSCh. 4.5 - Prob. 38PSCh. 4.5 - Prob. 39PSCh. 4.5 - Prob. 40PSCh. 4.5 - Prob. 41PSCh. 4.5 - Prob. 42PSCh. 4.5 - Prob. 43PSCh. 4.5 - Prob. 44PSCh. 4.5 - Prob. 45PSCh. 4.5 - Prob. 46PSCh. 4.5 - Prob. 47PSCh. 4.5 - Prob. 48PSCh. 4.5 - Prob. 49PSCh. 4.5 - Prob. 50PSCh. 4.5 - Prob. 51PSCh. 4.5 - Prob. 52PSCh. 4.5 - Prob. 53PSCh. 4.5 - Prob. 54PSCh. 4.5 - Prob. 55PSCh. 4.5 - Prob. 56PSCh. 4.5 - Prob. 57PSCh. 4.5 - Prob. 58PSCh. 4.5 - Prob. 59PSCh. 4.5 - Prob. 60PSCh. 4.6 - Prob. 1PSCh. 4.6 - Prob. 2PSCh. 4.6 - Prob. 3PSCh. 4.6 - Prob. 4PSCh. 4.6 - Prob. 5PSCh. 4.6 - Prob. 6PSCh. 4.6 - Prob. 7PSCh. 4.6 - Prob. 8PSCh. 4.6 - Prob. 9PSCh. 4.6 - Prob. 10PSCh. 4.6 - Prob. 11PSCh. 4.6 - Prob. 12PSCh. 4.6 - Prob. 13PSCh. 4.6 - Prob. 14PSCh. 4.6 - Prob. 15PSCh. 4.6 - Prob. 16PSCh. 4.6 - Prob. 17PSCh. 4.6 - Prob. 18PSCh. 4.6 - Prob. 19PSCh. 4.6 - Prob. 20PSCh. 4.6 - Prob. 21PSCh. 4.6 - Prob. 22PSCh. 4.6 - Prob. 23PSCh. 4.6 - Prob. 24PSCh. 4.6 - Prob. 25PSCh. 4.6 - Prob. 26PSCh. 4.6 - Prob. 27PSCh. 4.6 - Prob. 28PSCh. 4.6 - Prob. 29PSCh. 4.6 - Prob. 30PSCh. 4.6 - Prob. 31PSCh. 4.6 - Prob. 32PSCh. 4.6 - Prob. 33PSCh. 4.6 - Prob. 34PSCh. 4.6 - Prob. 35PSCh. 4.6 - Prob. 36PSCh. 4.6 - Prob. 37PSCh. 4.6 - Prob. 38PSCh. 4.6 - Prob. 39PSCh. 4.6 - Prob. 40PSCh. 4.6 - Prob. 41PSCh. 4.6 - Prob. 42PSCh. 4.6 - Prob. 43PSCh. 4.6 - Prob. 44PSCh. 4.6 - Prob. 45PSCh. 4.6 - Prob. 46PSCh. 4.6 - Prob. 47PSCh. 4.6 - Prob. 48PSCh. 4.6 - Prob. 49PSCh. 4.6 - Prob. 50PSCh. 4.6 - Prob. 51PSCh. 4.6 - Prob. 52PSCh. 4.6 - Prob. 53PSCh. 4.6 - Prob. 54PSCh. 4.6 - Prob. 55PSCh. 4.6 - Prob. 56PSCh. 4.6 - Prob. 57PSCh. 4.6 - Prob. 58PSCh. 4.6 - Prob. 59PSCh. 4.6 - Prob. 60PSCh. 4.7 - Prob. 1PSCh. 4.7 - Prob. 2PSCh. 4.7 - Prob. 3PSCh. 4.7 - Prob. 4PSCh. 4.7 - Prob. 5PSCh. 4.7 - Prob. 6PSCh. 4.7 - Prob. 7PSCh. 4.7 - Prob. 8PSCh. 4.7 - Prob. 9PSCh. 4.7 - Prob. 10PSCh. 4.7 - Prob. 11PSCh. 4.7 - Prob. 12PSCh. 4.7 - Prob. 13PSCh. 4.7 - Prob. 14PSCh. 4.7 - Prob. 15PSCh. 4.7 - Prob. 16PSCh. 4.7 - Prob. 17PSCh. 4.7 - Prob. 18PSCh. 4.7 - Prob. 19PSCh. 4.7 - Prob. 20PSCh. 4.7 - Prob. 21PSCh. 4.7 - Prob. 22PSCh. 4.7 - Prob. 23PSCh. 4.7 - Prob. 24PSCh. 4.7 - Prob. 25PSCh. 4.7 - Prob. 26PSCh. 4.7 - Prob. 27PSCh. 4.7 - Prob. 28PSCh. 4.7 - Prob. 29PSCh. 4.7 - Prob. 30PSCh. 4.7 - Prob. 31PSCh. 4.7 - Prob. 32PSCh. 4.7 - Prob. 33PSCh. 4.7 - Prob. 34PSCh. 4.7 - Prob. 35PSCh. 4.7 - Prob. 36PSCh. 4.7 - Prob. 37PSCh. 4.7 - Prob. 38PSCh. 4.7 - Prob. 39PSCh. 4.7 - Prob. 40PSCh. 4.7 - Prob. 41PSCh. 4.7 - Prob. 42PSCh. 4.7 - Prob. 43PSCh. 4.7 - Prob. 44PSCh. 4.7 - Prob. 45PSCh. 4.7 - Prob. 46PSCh. 4.7 - Prob. 47PSCh. 4.7 - Prob. 48PSCh. 4.7 - Prob. 49PSCh. 4.7 - Prob. 50PSCh. 4.7 - Prob. 51PSCh. 4.7 - Prob. 52PSCh. 4.7 - Prob. 53PSCh. 4.7 - Prob. 54PSCh. 4.7 - Prob. 55PSCh. 4.7 - Prob. 56PSCh. 4.7 - Prob. 57PSCh. 4.7 - Prob. 58PSCh. 4.7 - Prob. 59PSCh. 4.7 - Prob. 60PSCh. 4 - Prob. 1PECh. 4 - Prob. 2PECh. 4 - Prob. 3PECh. 4 - Prob. 4PECh. 4 - Prob. 5PECh. 4 - Prob. 6PECh. 4 - Prob. 7PECh. 4 - Prob. 8PECh. 4 - Prob. 9PECh. 4 - Prob. 10PECh. 4 - Prob. 11PECh. 4 - Prob. 12PECh. 4 - Prob. 13PECh. 4 - Prob. 14PECh. 4 - Prob. 15PECh. 4 - Prob. 16PECh. 4 - Prob. 17PECh. 4 - Prob. 18PECh. 4 - Prob. 19PECh. 4 - Prob. 20PECh. 4 - Prob. 21PECh. 4 - Prob. 22PECh. 4 - Prob. 23PECh. 4 - Prob. 24PECh. 4 - Prob. 25PECh. 4 - Prob. 26PECh. 4 - Prob. 27PECh. 4 - Prob. 28PECh. 4 - Prob. 29PECh. 4 - Prob. 30PECh. 4 - Prob. 1SPCh. 4 - Prob. 2SPCh. 4 - Prob. 3SPCh. 4 - Prob. 4SPCh. 4 - Prob. 5SPCh. 4 - Prob. 6SPCh. 4 - Prob. 7SPCh. 4 - Prob. 8SPCh. 4 - Prob. 9SPCh. 4 - Prob. 10SPCh. 4 - Prob. 11SPCh. 4 - Prob. 12SPCh. 4 - Prob. 13SPCh. 4 - Prob. 14SPCh. 4 - Prob. 15SPCh. 4 - Prob. 16SPCh. 4 - Prob. 17SPCh. 4 - Prob. 18SPCh. 4 - Prob. 19SPCh. 4 - Prob. 20SPCh. 4 - Prob. 21SPCh. 4 - Prob. 22SPCh. 4 - Prob. 23SPCh. 4 - Prob. 24SPCh. 4 - Prob. 25SPCh. 4 - Prob. 26SPCh. 4 - Prob. 27SPCh. 4 - Prob. 28SPCh. 4 - Prob. 29SPCh. 4 - Prob. 30SPCh. 4 - Prob. 31SPCh. 4 - Prob. 32SPCh. 4 - Prob. 33SPCh. 4 - Prob. 34SPCh. 4 - Prob. 35SPCh. 4 - Prob. 36SPCh. 4 - Prob. 37SPCh. 4 - Prob. 38SPCh. 4 - Prob. 39SPCh. 4 - Prob. 40SPCh. 4 - Prob. 41SPCh. 4 - Prob. 42SPCh. 4 - Prob. 43SPCh. 4 - Prob. 44SPCh. 4 - Prob. 45SPCh. 4 - Prob. 46SPCh. 4 - Prob. 47SPCh. 4 - Prob. 48SPCh. 4 - Prob. 49SPCh. 4 - Prob. 50SPCh. 4 - Prob. 51SPCh. 4 - Prob. 52SPCh. 4 - Prob. 53SPCh. 4 - Prob. 54SPCh. 4 - Prob. 55SPCh. 4 - Prob. 56SPCh. 4 - Prob. 57SPCh. 4 - Prob. 58SPCh. 4 - Prob. 59SPCh. 4 - Prob. 60SPCh. 4 - Prob. 61SPCh. 4 - Prob. 62SPCh. 4 - Prob. 63SPCh. 4 - Prob. 64SPCh. 4 - Prob. 65SPCh. 4 - Prob. 66SPCh. 4 - Prob. 67SPCh. 4 - Prob. 68SPCh. 4 - Prob. 69SPCh. 4 - Prob. 70SPCh. 4 - Prob. 71SPCh. 4 - Prob. 72SPCh. 4 - Prob. 73SPCh. 4 - Prob. 74SPCh. 4 - Prob. 75SPCh. 4 - Prob. 76SPCh. 4 - Prob. 77SPCh. 4 - Prob. 78SPCh. 4 - Prob. 79SPCh. 4 - Prob. 80SPCh. 4 - Prob. 81SPCh. 4 - Prob. 82SPCh. 4 - Prob. 83SPCh. 4 - Prob. 84SPCh. 4 - Prob. 85SPCh. 4 - Prob. 86SPCh. 4 - Prob. 87SPCh. 4 - Prob. 88SPCh. 4 - Prob. 89SPCh. 4 - Prob. 90SPCh. 4 - Prob. 91SPCh. 4 - Prob. 92SPCh. 4 - Prob. 93SPCh. 4 - Prob. 94SPCh. 4 - Prob. 95SPCh. 4 - Prob. 96SPCh. 4 - Prob. 97SPCh. 4 - Prob. 98SPCh. 4 - Prob. 99SP
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY