CALCULUS, VOLUME 1 (OER)17th EditionOpenStax Publisher: XANEDU CISBN: 2810022307715
CALCULUS, VOLUME 1 (OER)
Solutions for CALCULUS,VOLUME 1 (OER)
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....Problem 336E:
In the following exercises, find each indefinite integral by using appropriate substitutions....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=1 to ex and evaluate die...Problem 347E:
Write an integral to express the area under the graph of y=et between t=0 and t=Inx , and evaluate...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-end point approximation overestimate or underestimate the...Problem 367E:
In the following exercises, does the right-end point approximation overestimate or underestimate the...Problem 368E:
In the following exercises, does the right-end point approximation overestimate or underestimate the...Problem 369E:
In the following exercises, does the right-end point approximation overestimate or underestimate the...Problem 370E:
In the following exercises, does the right-end point approximation overestimate or underestimate the...Problem 371E:
In the following exercises, does the right-end point 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 infinity, of the area under the graph of f(x)=xex2 between x=0 and x=5...Problem 379E:
Show that abdtt= 1/b 1/a dt t 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 the...Problem 381E:
Use the previous exercise to find the derivative of h(x)=xx(1+Inx) and evaluate 23xx(1+Inx)dx .Problem 382E:
Show that if c0 , then the integral of 1/x from ac to bc (0ab) is the same as the integral of 1/x...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:
Use the identity Inx=1xdtx show that In(x) is an increasing function of x on [0,) , and use the...Problem 386E:
Pretend, for the moment, that we do not know that ex is the inverse function of In(x) , but keep in...Problem 387E:
Pretend, for the moment, that we do not know that ex is die inverse function of Inx , 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 - 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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