Q. 6 For each integral in Exercises 5... [FREE SOLUTION]

Chapter 5: Q. 6 (page 417)

For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.
$鈭� u^{2} d u$

Short Answer

Expert verified

The three integrals $鈭� \sin x {(\cos x)}^{2} d x, 鈭� \frac{{(\ln x)}^{2}}{x} d x and 鈭� (2 x + 1) (x^{2} + x) d x$ will have form $鈭� u^{2} d u$ after a substitution of variables.

Step by step solution

Step 1. Given Information

For given integral we have to write down three integrals that will have that form after a substitution of variables.
$鈭� u^{2} d u$

Step 2. The first integrals that will have that form after a substitution of variables.

Let

$u = \cos x \frac{d u}{d x} = \sin x d u = \sin x d x$

This substitution changes the integral into

$鈭� \sin x {(\cos x)}^{2} d x$

Step 3. The first integrals that will have that form after a substitution of variables.

Let

$u = \ln x \frac{d u}{d x} = \frac{1}{x} d u = \frac{1}{x} d x$

This substitution changes the integral into

$鈭� \frac{{(\ln x)}^{2}}{x} d x$

Step 4. The first integrals that will have that form after a substitution of variables.

Let

$u = x^{2} + x \frac{d u}{d x} = 2 x + 1 d u = (2 x + 1) d x$

This substitution changes the integral into

$鈭� (2 x + 1) (x^{2} + x) d x$

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91影视

For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.
$鈭� u^{2} d u$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The first integrals that will have that form after a substitution of variables.

Step 3. The first integrals that will have that form after a substitution of variables.

Step 4. The first integrals that will have that form after a substitution of variables.

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91影视

For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.鈭�u2du

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The first integrals that will have that form after a substitution of variables.

Step 3. The first integrals that will have that form after a substitution of variables.

Step 4. The first integrals that will have that form after a substitution of variables.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Geometry

Pure Maths

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.
$鈭� u^{2} d u$