CALCULUS, VOLUME 1 (OER)17th EditionOpenStax Publisher: XANEDU CISBN: 2810022307715
CALCULUS, VOLUME 1 (OER)
Solutions for CALCULUS,VOLUME 1 (OER)
Problem 254E:
Why is u-substitution referred to as change of variable?Problem 255E:
2. If f=gh, when reversing the chain title, ddx(gh)(x)=g(h(x))hx , 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 x2...Problem 266E:
In the following exercises, find the antiderivative using the indicated substitution. 266. x 1x2...Problem 267E:
In the following exercises, find the antiderivative using the indicated substitution. 267. (x1)( x2...Problem 268E:
In the following exercises, find the antiderivative using the indicated substitution. 268. (x22x)(...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...Problem 294E:
In the following exercises, use a change of variables to evaluate the definite integral. 294. 02t...Problem 295E:
In the following exercises, use a change of variables to evaluate the definite integral. 295. 01t2...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 average value of f(x) over an interval [a,b] is the same as the average value of f(cx)...Problem 314E:
Find the area under the graph of f(t)=t(1+ t 2)a between t=0 and t=x where a0 and a1 is fixed, and...Problem 315E:
Find the area under the graph of g(t)=t(1 t 2)a between t=0 and t=x , where 0x1 and a0 is fixed....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=1 to a and with a...Browse All Chapters of This Textbook
Chapter 1 - Functions And GraphsChapter 1.1 - Review Of FunctionsChapter 1.2 - Basic Classes Of FunctionsChapter 1.3 - Trigonometric FunctionsChapter 1.4 - Inverse FunctionsChapter 1.5 - Exponential And Logarithmic FunctionsChapter 2 - LimitsChapter 2.1 - A Preview Of CalculusChapter 2.2 - The Limit Of A FunctionChapter 2.3 - The Limit Laws
Chapter 2.4 - ContinuityChapter 2.5 - The Precise Definition Of A LimitChapter 3 - DerivativesChapter 3.1 - Defining The DerivativeChapter 3.2 - The Derivative As A FunctionChapter 3.3 - Differentiation RulesChapter 3.4 - Derivatives As Rates Of ChangeChapter 3.5 - Derivatives Of Trigonometric FunctionsChapter 3.6 - The Chain RuleChapter 3.7 - Derivatives Of Inverse FunctionsChapter 3.8 - Implicit DifferentiationChapter 3.9 - Derivatives Of Exponential And Logarithmic FunctionsChapter 4 - Applications Of DerivativesChapter 4.1 - Related RatesChapter 4.2 - Linear Approximations And DifferentialsChapter 4.3 - Maxima And MinimaChapter 4.4 - The Mean Value TheoremChapter 4.5 - Derivatives And The Shape Of A GraphChapter 4.6 - Limits At Infinity And AsymptotesChapter 4.7 - Applied Optimization ProblemsChapter 4.8 - L'hopitars RuleChapter 4.9 - Newton's MethodChapter 4.10 - AntiderivativesChapter 5 - IntegrationChapter 5.1 - Approximating AreasChapter 5.2 - The Definite IntegralChapter 5.3 - The Fundamental Theorem Of CalculusChapter 5.4 - Integration Formulas And The Net Change TheoremChapter 5.5 - SubstitutionChapter 5.6 - Integrals Involving Exponential And Logarithmic FunctionsChapter 5.7 - Integrals Resulting In Inverse Trigonometric FunctionsChapter 6 - Applications Of IntegrationChapter 6.1 - Areas Between CurvesChapter 6.2 - Determining Volumes By SlicingChapter 6.3 - Volumes Of Revolution: Cylindrical ShellsChapter 6.4 - Arc Length Of A Curve And Surface AreaChapter 6.5 - Physical ApplicationsChapter 6.6 - Moments And Centers Of MassChapter 6.7 - Integrals, Exponential Functions, And LogarithmsChapter 6.8 - Exponential Growth And DecayChapter 6.9 - Calculus Of The Hyperbolic Functions
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