Question

Evaluate the integral. $$ \int y e^{0.2 y} d y $$

   Evaluate the integral.
$$
\int y e^{0.2 y} d y
$$

Calculus Early Transcendentals 2

Calculus Early Transcendentals 2

James Stewart 8th Edition

Chapter 7, Problem 4

Instant Answer

Solved by Expert Robert Daugherty

05/14/2020

Step 1

The integral \(\int y e^{0.2 y} \, dy\) is a product of a polynomial function \(y\) and an exponential function \(e^{0.2y}\). This suggests that integration by parts is a suitable method. Show more…

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Evaluate the integral. $$ \int y e^{0.2 y} d y $$

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Key Concepts

Integration by Parts

Integration by parts is a fundamental technique used for integrating products of functions. It is based on the product rule for differentiation and allows one to convert an integral into another potentially simpler integral. The method involves choosing one part of the product to differentiate (often a polynomial) and the other part to integrate (often an exponential or trigonometric function), thus simplifying the overall integration process.

Exponential Function Integration

Integrating exponential functions is a central concept in calculus. Exponential functions have the unique property that their derivative is proportional to the function itself. When integrated in combination with other types of functions, such as polynomial terms, special techniques like integration by parts are often used to manage the integration process efficiently.

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