Chapter 5: Q. 4 (page 441)
Explain how to use long division to write the improper fraction as the sum of an integer and a proper fraction.
Short Answer
The required value is
Chapter 5: Q. 4 (page 441)
Explain how to use long division to write the improper fraction as the sum of an integer and a proper fraction.
The required value is
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Suppose v(x) is a function of x. Explain why the integral
of dv is equal to v (up to a constant).
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.
Find three integrals in Exercises 39–74 that can be solved by using a trigonometric substitution of the form .
List 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)?
Solve the integral :
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