Chapter 5: Q. 5 (page 417)
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
Short Answer
The three integrals will have form after a substitution of variables.
Chapter 5: Q. 5 (page 417)
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
The three integrals will have form after a substitution of variables.
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Get started for freeSolve the following two ways:
(a) with the trigonometric substitution x = 3 tan u;
(b) with algebra and the derivative of the arctangent.
Find three integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x).
Solve the integral
Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
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.
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