Question

Evaluate the integral. $\int t \sinh m t d t$

   Evaluate the integral.
 $\int t \sinh m t d t$

Calculus

James Stewart 7th Edition

Chapter 7, Problem 16

Instant Answer

Solved by Expert Foster Wisusik

10/21/2020

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Step 1: We need to evaluate the integral $\int t \sinh(mt) \, dt$. Show more…

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Evaluate the integral. $\int t \sinh m t d t$

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Key Concepts

Integration by Parts

Integration by parts is a fundamental technique in calculus used to integrate products of functions. It is based on the product rule for differentiation and provides a method to express the integral of a product of two functions in terms of the integral of their derivative and another function. This technique is especially useful when one part of the integrand becomes simpler upon differentiation, while the other part remains manageable upon integration.

Hyperbolic Functions

Hyperbolic functions, such as the hyperbolic sine and cosine functions, are analogues of the trigonometric functions but are defined using exponential functions. They satisfy identities similar to those in trigonometry and arise naturally in problems involving hyperbolas, differential equations, and many areas of applied mathematics. Understanding their properties, derivatives, and integrals is essential when dealing with integrals that involve hyperbolic functions.

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