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Chapter 5: Q. 22 (page 464)

In Exercises 20鈥�27, use reference triangles and the unit circle to write the given trigonometric compositions as algebraic functions.

tansin鈭�1x3

Short Answer

Expert verified

Ans:tansin鈭�1x3=x9-x2

Step by step solution

01

Step 1.Given information:

tansin鈭�1x3

02

Step 2. Finding the integrals using trigonometric substitution:

The reference triangle is as follows:

So,tansin-1x3=tanu=oppadj=x9-x2

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Most popular questions from this chapter

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�9-x2xdx

Suppose v(x) is a function of x. Explain why the integral

of dv is equal to v (up to a constant).

Which of the integrals that follow would be good candidates for trigonometric substitution? If a trigonometric substitution is a good strategy, name the substitution. If another method is a better strategy, explain that method.

(a)鈭�4+x2xdx (b)鈭�x4+x2dx

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Solve the integral:鈭�3-xe2xdx

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
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