Calculus Volume 22nd EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStax College.ISBN: 9781630182021
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
Sample Solutions for this Textbook
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More Editions of This Book
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Calculus Volume 2 by OpenStax
17th Edition
ISBN: 9781506698076
Calculus Volume 2
17th Edition
ISBN: 9781938168062
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