Chapter 5: Q. 18 (page 464)

Find three integrals in Exercises 39–74 that can be solved by using a trigonometric substitution of the form $x = a \tan u$ .

Short Answer

Expert verified

Ans:

\int \frac{1}{x^{2} - 4 x + 13} d x f o r 53 \int \frac{1}{\sqrt{x^{2} + 9}} d x f o r 56 \int \sqrt{x^{2} - 8 x + 25} d x f o r 57

Step by step solution

Step 1. Given information:

$x = a \tan u$

Step 2. Finding the three integrals using trigonometric substitution :

The three integrals that can be solved using a trigonometric substitution of the form $x = a$ tan $u$ are the exercises 53,56 and 57.

The integrals are as follows.

53. $\int \frac{1}{x^{2} - 4 x + 13} d x$

56. $\int \frac{1}{\sqrt{x^{2} + 9}} d x$

57. $\int \sqrt{x^{2} - 8 x + 25} d x$

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Find three integrals in Exercises 39–74 that can be solved by using a trigonometric substitution of the form $x = a \tan u$ .

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Finding the three integrals using trigonometric substitution :

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Find three integrals in Exercises 39–74 that can be solved by using a trigonometric substitution of the form x=atanu.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Finding the three integrals using trigonometric substitution :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Decision Maths

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find three integrals in Exercises 39–74 that can be solved by using a trigonometric substitution of the form $x = a \tan u$ .