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Chapter 5: Q. 36 (page 478)

Use limits of definite integrals to calculate each of the improper integrals in Exercises.

鈭�0鈭�xe-xdx

Short Answer

Expert verified

The improper integral on [0,鈭�]converges.

鈭�0鈭�xe-xdx=1.

Step by step solution

01

Step 1. Given information. 

The given integral is the following.

鈭�0鈭�xe-xdx

02

Step 2. Value of integral. 

Solve the integral by using the definition of improper integral.

鈭�0鈭�xe-xdx=lima鈫�鈭�鈭�0axe-xdx=lima鈫�鈭�-xe-x-e-x0a=lima鈫�鈭�-ae-a-e-a-(-1)=0+1=1

The value of the integral is鈭�0鈭�xe-xdx=1.

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