Calculus Volume 217th EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStaxISBN: 9781938168062
Calculus Volume 2
Solutions for Calculus Volume 2
Problem 254E:
Why is u-substitution referred to as change of variable?Problem 255E:
. If f=gh , when reversing the chain rule, ddx=(gh)=g(h(x))h(x) , should you take u=g(x) or u=h(x) ?Problem 256E:
In the following exercises, verify each identity using differentiation. Then, using the indicated...Problem 257E:
In the following exercises, verify each identity using differentiation. Then, using the indicated...Problem 258E:
In the following exercises, verify each identity using differentiation. Then, using the indicated...Problem 259E:
In the following exercises, verify each identity using differentiation. Then, using the indicated...Problem 260E:
In the following exercises, verify each identity using differentiation. Then, using the indicated...Problem 261E:
In the following exercises, find the antiderivative using the indicated substitution. 261. (...Problem 262E:
In the following exercises, find the antiderivative using the indicated substitution. 262. (...Problem 263E:
In the following exercises, find the antiderivative using the indicated substitution. 263. (...Problem 264E:
In the following exercises, find the antiderivative using the indicated substitution. 264. (...Problem 265E:
In the following exercises, find the antiderivative using the indicated substitution. 265. x x 2...Problem 266E:
In the following exercises, find the antiderivative using the indicated substitution. 266. x 1 x 2...Problem 267E:
In the following exercises, find the antiderivative using the indicated substitution. 267. (x1)( x 2...Problem 268E:
In the following exercises, find the antiderivative using the indicated substitution. 268. (x22x)( x...Problem 269E:
In the following exercises, find the antiderivative using the indicated substitution. 269....Problem 270E:
In the following exercises, find the antiderivative using the indicated substitution. 270....Problem 271E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 272E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 273E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 274E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 275E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 276E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 277E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 278E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 279E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 280E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 281E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 282E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 283E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 284E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 285E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 286E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 287E:
In the following Exercises, use a suitable change of variables to determine the indefinite integral....Problem 288E:
In the following Exercises, use a calculator to estimate the area under the curve using left Riemann...Problem 289E:
In the following Exercises, use a calculator to estimate the area under the curve using left Riemann...Problem 290E:
In the following Exercises, use a calculator to estimate the area under the curve using left Riemann...Problem 291E:
In the following Exercises, use a calculator to estimate the area under the curve using left Riemann...Problem 292E:
In the following exercises, use a change of variables to evaluate the definite integral. 292....Problem 293E:
In the following exercises, use a change of variables to evaluate the definite integral. 293. 01x 1+...Problem 294E:
In the following exercises, use a change of variables to evaluate the definite integral. 294. 02t 5...Problem 295E:
In the following exercises, use a change of variables to evaluate the definite integral. 295. 01t 1+...Problem 296E:
In the following exercises, use a change of variables to evaluate the definite integral. 296....Problem 297E:
In the following exercises, use a change of variables to evaluate the definite integral. 297. 0/4sin...Problem 298E:
In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using...Problem 299E:
In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using...Problem 300E:
In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using...Problem 301E:
In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using...Problem 302E:
In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using...Problem 303E:
In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using...Problem 306E:
In the following exercises, use a change of variables to show that each definite integral is equal...Problem 307E:
In the following exercises, use a change of variables to show that each definite integral is equal...Problem 308E:
In the following exercises, use a change of variables to show that each definite integral is equal...Problem 309E:
In the following exercises, use a change of variables to show that each definite integral is equal...Problem 310E:
In the following exercises, use a change of variables to show that each definite integral is equal...Problem 311E:
In the following exercises, use a change of variables to show that each definite integral is equal...Problem 312E:
In the following exercises, use a change of variables to show that each definite integral is equal...Problem 313E:
Show that the avenge value of f(x) over an interval [a, b] is the same as the average value of f(cx)...Problem 314E:
€314. Find the area under the graph of f(t)=t(1 t 2)a between t = 0 and t = x where a > 0 and a1 is...Problem 315E:
Find the area under the graph of g(t)=t(1 t 2)a between t = 0 and t = x, where 0 < x < 1 and a > 0...Problem 316E:
The area of a semicircle of radius 1 can be expressed as 111x2dx . Use the substitution x = cost to...Problem 317E:
The area of the top half of an ellipse with a major axis that is the x-axis from x = l to a and with...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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