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Chapter 5: Q. 19 (page 464)

Find three integrals in Exercises 39鈥�74 that can be solved without using trigonometric substitution.

Short Answer

Expert verified

Ans:

鈭�xx2-1dxfor41鈭�xx2+1dxfor42鈭�x2+9x32dxfor46

Step by step solution

01

Step 1. Given information:

Use trigonometric substitution

02

Step 2. Finding the three integrals using trigonometric substitution :

The three integrals that can be solved without using a trigonometric substitution are exercises 41,42 and 46.

The integrals are as follows.

41. 鈭�xx2-1dx

42. 鈭�xx2+1dx

46. 鈭�x2+9x32dx

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Most popular questions from this chapter

Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.

鈭�x4-32+3x2dx

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

鈭�xx2-1dx

Why doesn鈥檛 the definite integral鈭�231-x2dx make sense? (Hint: Think about domains.)

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)?

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.

x2鈭�4x鈭�8
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