Question

Evaluate the integral. $\int s 2^x d s$

   Evaluate the integral.
 $\int s 2^x d s$

Calculus

James Stewart 7th Edition

Chapter 7, Problem 14

Instant Answer

Solved by Expert Yiyang Wang

04/16/2022

Step 1

The integral given is \(\int s 2^x \, ds\). Here, \(s\) is the variable of integration, and \(2^x\) is treated as a constant with respect to \(s\). Show more…

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Evaluate the integral. $\int s 2^x d s$

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Key Concepts

Identification of Independent Variables

In expressions where the integrand contains terms involving variables different from the variable of integration, those terms are considered constants. Recognizing which parts of an integrand are independent of the integration variable is crucial for correctly applying integration techniques.

Integration of Polynomial Functions

Integrating a polynomial function involves applying the power rule, which states that the indefinite integral of a variable raised to a power is the variable raised to one higher power divided by that number, plus a constant of integration. This rule is fundamental in computing antiderivatives of polynomial terms.

Constant Multiple Rule in Integration

When integrating, any factor in the integrand that does not depend on the variable of integration can be treated as a constant and factored out of the integral. This simplifies the process by reducing the problem to integrating the remaining function.

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