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Chapter 5: Q. 35 (page 478)

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

鈭�0鈭�xe-x2dx

Short Answer

Expert verified

The improper integral on 0,鈭�converges.

鈭�0鈭�xe-x2dx=12

Step by step solution

01

Step 1. Given information. 

The given integral is the following.

鈭�0鈭�xe-x2dx

02

Step 2. Value of integral. 

Solve the integral by using the definition of improper integral.

鈭�0鈭�xe-x2dx=lima鈫�鈭�鈭�0axe-x2dx=lima鈫�鈭�-12e-x20a=lima鈫�鈭�-12e-a2--12=0+12=12

The value of the integral is鈭�0鈭�xe-x2dx=12

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