Chapter 5: Q. 29 (page 464)

Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
$x^{2} + 6 x - 2$

Short Answer

Expert verified

The completing square of the given quadratic equation is ${(x + 3)}^{2} - 11,$ and the appropriate trigonometric substitution is $x + 3 = \sqrt{11} s e c u .$

Step by step solution

Step 1. Given Information.

The given quadratic is $x^{2} + 6 x - 2 .$

Step 2. Completing the square for the given quadratic.

The complete square of the given quadratic equation is as follows:

$x^{2} + 6 x - 2 = x^{2} + 6 x + {(3)}^{2} - 2 - {(3)}^{2} = {(x + 3)}^{2} - 11$

Step 3. Describing the trigonometric substitution.

After completing the square for the given quadratic equation it is in the form of $x^{2} - a^{2} .$

So, for solving an integral that involved the quadratic then the trigonometric substitution can be used islocalid="1649054533258" $x = a s e c u .$

Here, $x = x + 3, a = \sqrt{11} .$

Thus, the appropriate trigonometric substitution islocalid="1649054515691" $x + 3 = \sqrt{11} s e c u .$

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Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
$x^{2} + 6 x - 2$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Completing the square for the given quadratic.

Step 3. Describing the trigonometric substitution.

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Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.x2+6x−2

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Completing the square for the given quadratic.

Step 3. Describing the trigonometric substitution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Statistics

Discrete Mathematics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
$x^{2} + 6 x - 2$