Chapter 5: Q. 7 (page 464)
Why don’t we ever have cause to use the trigonometric substitution ?
Short Answer
Ans: In terms of the Pythagorean identity, sine and cosine behave the same way. That's why we can always use instead of .
Chapter 5: Q. 7 (page 464)
Why don’t we ever have cause to use the trigonometric substitution ?
Ans: In terms of the Pythagorean identity, sine and cosine behave the same way. That's why we can always use instead of .
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Get started for freeList some things which would suggest that a certain substitution u(x) could be a useful choice. What do you look for when choosing u(x)?
Consider the integral .
(a) Solve this integral by using u-substitution.
(b) Solve the integral another way, using algebra to multiply out the integrand first.
(c) How must your two answers be related? Use algebra to prove this relationship.
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.
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 the integral:
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