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Chapter 5: Q. 45 (page 478)
Use limits of definite integrals to calculate each of the improper integrals in Exercises 21鈥�56.
The answer is.
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For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.
Explain why using trigonometric substitution with often involves a triangle with side lengths a and x and hypotenuse of length
Complete the square for each quadratic in Exercises 28鈥�33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.
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 ?
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