Chapter 8.8, Problem 80E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Gravitational Force A “semi-infinite” uniform rod occupies the nonnegative x-axis. The rod has a linear density δ , which means that a segment of length dx has a mass of δ dx. A particle of mass M is located at the point (-a, 0). The gravitational force F that the rod exerts on the mass is given by F = ∫ 0 ∞ G M δ ( a + x ) 2 d x where G is the gravitational constant. Find F.

To determine

To calculate: The value of gravitational force F=0GMδ(a+x)2dx

Explanation

Given:

The gravitational force F is:

F=âˆ«0âˆžGMÎ´(a+x)2dx

Where G, M, and Î´ are constant.

Formula used:

For the convergence, the following limit must exist.

âˆ«abf(x)dx=limbâ†’âˆžâˆ«abf(x)dx

Calculation:

Consider the provided function,

F=âˆ«0âˆžGMÎ´(a+x)2dx=limbâ†’âˆžâˆ«0b

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