Chapter 5: Q. 10 (page 417)
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Short Answer
The differential du in terms of the differential dxis .
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Chapter 5: Q. 10 (page 417)
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
The differential du in terms of the differential dxis .
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Solve the integral:
Give an example of an integral for which trigonometric substitution is possible but an easier method is available. Then give an example of an integral that we still don’t know how to solve given the techniques we know at this point.
Solve the integralthree ways:
(a) with the substitution followed by back substitution;
(b) with integration by parts, choosing localid="1648814744993"
(c) with the trigonometric substitution x = sec u.
Explain how to use long division to write the improper fraction as the sum of an integer and a proper fraction.
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
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