Chapter 5: Q. 8 (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. 8 (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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Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution withor ? Why do we need to think about the unit circle after trigonometric substitution with ?
Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
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.
Show that if , then , in the following two ways: (a) by using implicit differentiation, thinking of as a function of , and (b) by thinking of as a function of .
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