Solve the Problem $y = \tanh x$ , Below by The $x$

question 56

Multiple Choice

Solve the problem.
-A region in the first quadrant is bounded above by the curve $y = \tanh x$ , below by the $x$ -axis, on the left by the $y$ -axis, and on the right by the line $x = \ln 5$ . Find the volume of the solid generated by revolving the region about the $x$ -axis.

• A) \(2 \pi\)
• B) \(- \frac { 12 } { 13 }\)
• C) \(\pi \left( \ln 5 - \frac { 12 } { 13 } \right)\)
• D) 0

---

Definitions:

Analytic Cognitive Style

A style of thinking characterized by a logical, detail-oriented, and systematic approach to problem-solving and decision-making.

Mental Shortcuts

Heuristic techniques used by individuals to simplify decision-making processes, though they may not always lead to accurate judgments.

Step-by-Step Procedures

Detailed, sequential instructions designed to guide someone through the completion of a task or process.

Incubation Effect

A phenomenon in problem-solving where a solution or creative insight comes to mind after taking a break from focused work on the problem.