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Topic: Trigonometric substitution


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In the News (Sat 20 Jul 19)

  
  PlanetMath: a lecture on integration by substitution
This function is also a typical example of integration with substitution.
See Also: a lecture on integration by parts, A lecture on trigonometric integrals and trigonometric substitution, a lecture on the partial fraction decomposition method
This is version 1 of a lecture on integration by substitution, born on 2006-01-26.
planetmath.org /encyclopedia/ALectureOnIntegrationBySubstitution.html   (253 words)

  
 Karl's Calculus Tutor - 11.5 Trigonometric Substitution
Trigonometric substitution is a big topic because there are lots of variations.
Here is an integrand that you've seen before because it's on the table, but it is useful to see how we can use a trigonometric substitution on it.
In the mean time, all the integrands that you can integrate using the expanded trig substitutions will also yield to Hyperbolic Substitution, which is the next section.
www.karlscalculus.org /calc11_4.html   (2745 words)

  
 PlanetMath: A lecture on trigonometric integrals and trigonometric substitution
A lecture on trigonometric integrals and trigonometric substitution
This is the prototype of integral where a trigonometric substitution will work very nicely.
This is version 1 of A lecture on trigonometric integrals and trigonometric substitution, born on 2006-01-31.
planetmath.org /encyclopedia/ALectureOnTrigonometricIntegralsAndTrigonometricSubstitution.html   (398 words)

  
 Trigonometric Substitutions - HMC Calculus Tutorial
The sketch of the triangle is very useful for determining what substitution should be made.
A trigonometric substitution will not always be necessary, even when the types of factors seen above appear.
Trigonometric substitutions are often useful for integrals containing factors of the form
www.math.hmc.edu /calculus/tutorials/trig_substitution   (260 words)

  
 Karl's Calculus Tutor - 11.5 Hyperbolic Substitution
If hyperbolic substitution is not part of your curriculum, then skip ahead (unless you're curious) to Partial Fractions, and don't worry, we will cover the methods to integrate the functions that are covered here later on.
Indeed we later found that by completing the square we could use this same substitution to integrate a whole class of functions that had a quadratic under the radical -- but not all such functions.
Despite all these differences, these functions provide the substitutions we need to integrate a whole family of integrands that trig substitutions are able to address only in a clumsy way.
www.karlscalculus.org /hyper.html   (2129 words)

  
 Quiz 2
By the end of [worksheet 8] you will be familiar with the many trigonometric identities that can be useful in evaluating integrals with trigonometric integrands.
In this worksheet, substitution, integration by parts, and the many trigonometric identities are the tools that you can use.
The tools you have available for this worksheet are substitution, integration by parts, trigonometric identities, and partial fraction decomposition.
www.math.uiuc.edu /~mjames2/fa05math230/quiz2.html   (400 words)

  
 Trigonometric substitution - Wikipedia, the free encyclopedia
In mathematics, trigonometric substitution is the substitution of trigonometric functions for other expressions.
If we had missed this restriction, we might have picked θ to go from π to 5π/6, which would result in the negative of the result.)
Substitution can be used to remove trigonometric functions.
en.wikipedia.org /wiki/Trigonometric_substitution   (245 words)

  
 Mathlets: Substitution 2
Enter the substitution function g(x) in the text input field marked "u=g(x)=", and its derivative g'(x) in the text input field marked "u'=g'(x)=".
The graph on the left shows f (x), and the graph on the right shows the effect making the substitution u=g(x), so plotting the curve given by points of the form (g(x), f (x)/g'(x)).
With the two graphs giving different heights, and the base width in the left graph fixed by the text input field, the critical dimension is the base width in the right graph -- this is the effect of the substitution u=g(x).
cs.jsu.edu /mcis/faculty/leathrum/Mathlets/subst2.html   (517 words)

  
 Hints: UNT Integration Bee   (Site not responding. Last check: 2007-10-13)
Substitute u = x + 4, then multiply out.
Substitute u = x + 3; expand; integrate term by term.
Substitute x = sin t; then substitute u = tan(t/2).
members.cox.net /hwarchall/IntegrationBee/BeeProblemsHints.html   (244 words)

  
 Mathematical Sciences, Undergraduate Course Descriptions
Functions, limits, derivatives, logarithmic, exponential, and trigonometric functions, inverse functions; L'Hospital's Rule, curve sketching, Mean Value Theorem, related rates, linear and quadratic approximations, maximum-minimum problems, inverse functions, definite and indefinite integrals, and hyperbolic functions; applications of integration, integration by substitution and by parts.
Integration by trigonometric substitution and partial fractions; arclength; improper integrals; Simpson's and Trapezoidal Rules for numerical integration; separable differential equations, first order linear differential equations, homogeneous second order linear differential equations with constant coefficients.
Integration by trigonometric substitution and partial fractions; arclength; improper integrals; Simpson's and Trapezoidal Rules for numerical integration; separable differential equations, first order linear differential equations, homogeneous second order linear differential equations with constant coefficients; series solution, Newton's method, Taylor's Theorem including a discussion of the remainder, sequences, series, power series;.
www.math.cmu.edu /ug/courses/courses-desc.html   (2856 words)

  
 Trigonometric Substitutions
Substitutions allow us to solve complicated-looking integrals by converting them into something more manageable.
     Now, we shall examine a different type of substitution: a trigonometric substitution, which will allow us to integrate more functions.
     Often times, though, we will need to complete the square to use a trigonometric substitution.
math.ucsd.edu /~wgarner/math10b/trig_sub.htm   (293 words)

  
 CALCULUS II   EXAM II NOTES AND LINKS
Here are links to some tutorials on trigonometric integrals: Powers and products of sines and cosines, more products of sines and cosines, other trig powers, rational expressions of trig functions.
Here is what Karl's Calculus Tutor has to say about trigonometric substitution and here is HMC on trig substitutions.
Here are some drill problems involving trigonometric substitution.
www2.scc-fl.edu /lvosbury/CalculusII_Folder/Calculus_II_Exam_2.htm   (774 words)

  
 Mathlets: Substitution 1
Graphs a function f (x), the area under the graph of f (x) for a given interval, and the modifications made to f (x) and the area by a substitution u=g(x)
The area under the graph of f (x) is drawn with the area under the curve on the interval [a,b] shaded so that positive areas are
The graph on the left shows the areas after making the substitution u=g(x), so plotting (g(x), f (x)/g'(x)) for x in the interval [a,b].
cs.jsu.edu /mcis/faculty/leathrum/Mathlets/subst.html   (344 words)

  
 Trigonometric Techniques of Integration
Suppose a friend in your calculus class tells you that this section just has too many rules to memorize.
Without memorizing rules, you can remember a small number of potential substitutions and see which one works for a given problem.
In exercises 41 and 42, evaluate the integral using both substitutions u = tanx and u = secx and compare the results.
euphrates.wpunj.edu /courses/maen507/Week12/section03_exr.htm   (398 words)

  
 14 Coach, M252, Oregon State University
, particularly under a square root sign, then this is a possible case for integration by trigonometric substitution.
Use the triangle at the right to assist in using trig substitution.
Drill Problems using Trigonometric Substitution form Visual Calculus.
oregonstate.edu /instruction/mth252/cq2/Lesson09/coach.html   (86 words)

  
 174 Objectives
Memorize the integrals of the six basic trigonometric functions.
Use trigonometric substitution to evaluate integrals involving square roots of functions:
Integrate by using substitutions to convert some rational functions of sine and cosine into
courses.cvcc.vccs.edu /Math_Barringer/174-ob.htm   (1357 words)

  
 Mathematics Calculus Homework Help
I think the following problem uses the substitution: x=a tanθ replaces a²+ x² by a²sec²θ Please show all steps involved.
Please evaluate the following integral using trigonometric substitution.
Please evaluate the following integral using integration by trigonometric substitution.
www.brainmass.com /homework-help/math/calculus/pg195   (256 words)

  
 EMTeachline trigonometry software - trigonometric solutions - trigonometric tests
Fundamental identity, universal substitution, multiple arguments, reduction formulas and more.
Solution methods: Substitution, factoring, grouping, Bezout theorem, formulas of short multiplication, method of intervals and more.
Solution methods: universal substitution, sum, product and addition of trigonometric functions, power reduction, multiple argument, shift of argument and more.
www.emteachline.com /eng/fc29.htm   (3787 words)

  
 [No title]   (Site not responding. Last check: 2007-10-13)
You may have to make a u-substitution first.
Evaluate the integral  EMBED Equation.3  using a trigonometric substitution.
Evaluate the integral  EMBED Equation.3  using a trigonometric identity.
www.delta.edu /jaham/math162/hw2162ch8.doc   (491 words)

  
 Trigonometric substitutions
So from the above substitutions, we will set
The following examples illustrate how to use trigonometric substitutions :
Please post your question on our S.O.S. Mathematics CyberBoard.
www.sosmath.com /calculus/integration/trigsub/trigsub.html   (87 words)

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