Calculus Volume 22nd EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStax College.ISBN: 9781630182021
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
Sample Solutions for this Textbook
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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
17th Edition
ISBN: 9781938168062
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