Calculus Volume 217th EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStaxISBN: 9781938168062
Calculus Volume 2
Solutions for Calculus Volume 2
Problem 328E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 328....Problem 329E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 329....Problem 330E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 330....Problem 331E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 331....Problem 332E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 332....Problem 333E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 333....Problem 334E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 334....Problem 335E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 335....Problem 336E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 336....Problem 337E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 337....Problem 338E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 338....Problem 339E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 339....Problem 340E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 340....Problem 341E:
In the following exercises, find each indefinite integral by using appropriate substitutions. 341. e...Problem 342E:
In the following exercises, verify by differentiation that Inxdx=x(Inx1)+C , then use appropriate...Problem 343E:
In the following exercises, verify by differentiation that Inxdx=x(Inx1)+C , then use appropriate...Problem 344E:
In the following exercises, verify by differentiation that Inxdx=x(Inx1)+C , then use appropriate...Problem 345E:
In the following exercises, verify by differentiation that Inxdx=x(Inx1)+C , then use appropriate...Problem 346E:
Write an integral to express the area under the graph of y=1t from t = l to ex and evaluate the...Problem 347E:
Write an integral to express the area under the graph of y = et between t = 0 and t = Inx, and...Problem 348E:
In the following exercises, use appropriate substitutions to express the trigonometric integrals in...Problem 349E:
In the following exercises, use appropriate substitutions to express the trigonometric integrals in...Problem 350E:
In the following exercises, use appropriate substitutions to express the trigonometric integrals in...Problem 351E:
In the following exercises, use appropriate substitutions to express the trigonometric integrals in...Problem 352E:
In the following exercises, use appropriate substitutions to express the trigonometric integrals in...Problem 353E:
In the following exercises, use appropriate substitutions to express the trigonometric integrals in...Problem 354E:
In the following exercises, use appropriate substitutions to express the trigonometric integrals in...Problem 357E:
In the following exercises, evaluate the definite integral. 357. 0/3sinxcosxsinx+cosxdxProblem 360E:
In the following exercises, integrate using the indicated substitution. 360. xx100dx;u=x100Problem 361E:
In the following exercises, integrate using the indicated substitution. 361. y1y+1dy;u=y+1Problem 362E:
In the following exercises, integrate using the indicated substitution. 362. 1x23xx3dx;u=3xx3Problem 364E:
In the following exercises, integrate using the indicated substitution. 364. e2x1e 2xdx;u=e2xProblem 365E:
In the following exercises, integrate using the indicated substitution. 365. In(x) 1 ( Inx ) 2...Problem 366E:
In the following exercises, does the right-endpoint approximation overestimate or underestimate the...Problem 367E:
In the following exercises, does the right-endpoint approximation overestimate or underestimate the...Problem 368E:
In the following exercises, does the right-endpoint approximation overestimate or underestimate the...Problem 369E:
In the following exercises, does the right-endpoint approximation overestimate or underestimate the...Problem 370E:
In the following exercises, does the right-endpoint approximation overestimate or underestimate the...Problem 371E:
In the following exercises, does the right-endpoint approximation overestimate or underestimate the...Problem 372E:
In the following exercises, f(x)0 for axb . Find the area under the graph of f (x) between the given...Problem 373E:
In the following exercises, f(x)0 for axb . Find the area under the graph of f (x) between the given...Problem 374E:
In the following exercises, f(x)0 for axb . Find the area under the graph of f (x) between the given...Problem 375E:
In the following exercises, f(x)0 for axb . Find the area under the graph of f (x) between the given...Problem 377E:
Compute the integral of f(x)=xex2 and find the smallest value of N such that the area under the...Problem 378E:
Find the limit, as N tends to in?nity, of the area under the graph of f(x)=xex2 between x = 0 and x...Problem 379E:
Show that abdtt=1/b1/adtt when 0ab .Problem 380E:
Suppose that f(x) > 0 for all x and that f and g are differentiable. Use the identity fg=egInf and...Problem 381E:
Use the previous exercise to find the antiderivative of h(x)=xx(1+Inx) and evaluate 23xx(1+Inx)dx .Problem 382E:
Show that if c > 0, then the integral of l/x from ac to bc (0 < a < b) is the same as the integral...Problem 383E:
The following exercises are intended to derive the fundamental properties of the natural log...Problem 384E:
The following exercises are intended to derive the fundamental properties of the natural log...Problem 385E:
The following exercises are intended to derive the fundamental properties of the natural log...Problem 386E:
Pretend, fat the moment, that we do not know that ex is the inverse function of ln(x), but keep in...Problem 387E:
Pretend, fur the moment, that we do not know that ex is the inverse function of lnx, but keep in...Problem 388E:
The sine integral, defined as S(x)=0xsinttdt is an important quantity in engineering. Although it...Browse All Chapters of This Textbook
Chapter 1 - IntegrationChapter 1.1 - Approximating AreasChapter 1.2 - The Definite IntegralChapter 1.3 - The Fundamental Theorem Of CalculusChapter 1.4 - Integration Formulas And The Net Change TheoremChapter 1.5 - SubstitutionChapter 1.6 - Integrals Involving Exponential And Logarithmic FunctionsChapter 1.7 - Integrals Resulting In Inverse Trigonometric FunctionsChapter 2 - Applications Of IntegrationChapter 2.1 - Areas Between Curves
Chapter 2.2 - Determining Volumes By SlicingChapter 2.3 - Volumes Of Revolution: Cylindrical ShellsChapter 2.4 - Am Length Of A Curve And Surface AreaChapter 2.5 - Physical ApplicationsChapter 2.6 - Moments And Centers Of MassChapter 2.7 - Integrals, Exponential Functions, And LogarithmsChapter 2.8 - Exponential Growth And DecayChapter 2.9 - Calculus Of The Hyperbolic FunctionsChapter 3 - Techniques Of IntegrationChapter 3.1 - Integration By PartsChapter 3.2 - Trigonometric IntegralsChapter 3.3 - Trigonometric SubstitutionChapter 3.4 - Partial FractionsChapter 3.5 - Other Strategies For IntegrationChapter 3.6 - Numerical IntegrationChapter 3.7 - Improper IntegralsChapter 4 - Introduction To Differential EquationsChapter 4.1 - Basics Of Differential EquationsChapter 4.2 - Direction Fields And Numerical MethodsChapter 4.3 - Separable EquationsChapter 4.4 - The Logistic EquationChapter 4.5 - First-order Linear EquationsChapter 5 - Sequences And SeriesChapter 5.1 - SequencesChapter 5.2 - Infinite SeriesChapter 5.3 - The Divergence And Integral TestsChapter 5.4 - Comparison TestsChapter 5.5 - Alternating SeriesChapter 5.6 - Ratio And Root TestsChapter 6 - Power SeriesChapter 6.1 - Power Series And FunctionsChapter 6.2 - Properties Of Power SeriesChapter 6.3 - Taylor And Maclaurin SeriesChapter 6.4 - Working With Taylor SeriesChapter 7 - Parametric Equations And Polar CoordinatesChapter 7.1 - Parametric EquationsChapter 7.2 - Calculus Of Parametric CurvesChapter 7.3 - Polar CoordinatesChapter 7.4 - Area And Arc Length In Polar CoordinatesChapter 7.5 - Conic Sections
Book Details
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
Sample Solutions for this Textbook
We offer sample solutions for Calculus Volume 2 homework problems. See examples below:
More Editions of This Book
Corresponding editions of this textbook are also available below:
Calculus Volume 2 by OpenStax
17th Edition
ISBN: 9781506698076
Calculus Volume 2
2nd Edition
ISBN: 9781630182021
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