Explanation Given Information: The provided integral is ∫ 0 + ∞ e − x cos x d x . Consider the provided integral, ∫ 0 + ∞ e − x cos x d x , To evaluate the integral ∫ 0 + ∞ e − x cos x d x , suppose that the function u is cos x and v is e − x . Now, evaluate the D ( u ) , I ( v ) , and record in the table. The steps to create the table are shown below: In the table, in the column D, substitute the value of function u , and in the column I, substitute the value of v. The arrow shows the product of two terms such as cos x ( − e − x ) . Then, insert the value of D ( cos x ) = − sin x , and in the column I, insert the value of I ( − e − x ) = e − x The arrow shows the product of two terms such as − sin x e − x . The negative sign on the left of the table is indicating that the product is subtracted from the above product. Then, insert the value of D ( − sin x ) = − cos x in column D , the arrow shows the product of D ( − sin x ) = − cos x with I ( − e − x ) = e − x . Then the plus sign on the left of the table is used to indicate that the product will appear with positive sign in the formula. D I + cos x e − x - − sin x − e − x + ∫ − cos x e − x Now, read the values from the table and represented as ∫ e − x cos x d x = cos x ( − e − x ) − ( e − x ) ( − sin x ) − ∫ e − x cos x d x = − e − x cos x + ( e − x ) ( sin x ) − ∫ e − x cos x d x Further solved as, ∫ e − x cos x d x + ∫ e − x cos x d x = − e − x cos x + ( e − x ) ( sin x ) + C 2 ∫ e − x cos x d x = − e − x cos x + ( e − x ) ( sin x ) + C Divide both sides by 2 , ∫ e − x cos x d x = − 1 2 e − x cos x + 1 2 ( e − x ) ( sin x ) + C Determine the limit of the function

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 16.3, Problem 57E

To determine

Whether the integral ∫0+∞e−xcosx dx is converges or not, if it converges find the value of the integral ∫0+∞e−xcosx dx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.3, Problem 56E

Chapter 16.3, Problem 58E

Students have asked these similar questions

In Exercises 6–10, let f(x) = cos x, g(x) = Vx+ 2, and h(x) = 3x?. Write the given function as a composite of two or more of f, g, and h. For example, cos 3x? is f(h(x)). 6. V cos x + 2 1. V3 cos?x + 2 8. 3 cos x + 6 ). cos 27x* 10. cos V2 + 3x²,

In Exercises 31–36, find a general formula for f®)(x).

In Exercises 45–50, use Taylor’s Theorem to obtain an upper bound for the error of the approximation. Then calculate the exact value of the error

Chapter 16 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Whether the integral ∫ 0 + ∞ e − x cos x d x is converges or not, if it converges find the value of the integral ∫ 0 + ∞ e − x cos x d x .

Solution Summary: The author explains that the provided integral function is converges and the limit of the integral is 12.

Videos

Whether the integral ∫0+∞e−xcosx dx is converges or not, if it converges find the value of the integral ∫0+∞e−xcosx dx.

Want to see the full answer?

Chapter 16 Solutions