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Chapter 5: Q 20. (page 495)

Defining improper integrals: Fill in the blanks, using limits and proper definite integrals to express each of the following types of improper integrals.

If f is a continuous on -鈭�鈥�,鈭�, then for any real number c,

鈭�-鈭�鈭�fxdx=___+___

Short Answer

Expert verified

limd鈫�-鈭�鈭�dcfxdx+lime鈫�鈭�鈭�cefxdx

Step by step solution

01

Step 1. Given information.

Consider the given integral,

鈭�-鈭�鈭�fxdx

02

Step 2. Defining improper integrals.

Since the given function is continuous on the given interval -鈭�,鈭�. As c is any real number then break the integral interval to rewrite it.

鈭�-鈭�鈭�fxdx=鈭�-鈭�cfxdx+鈭�c鈭�fxdx=limd鈫�-鈭�鈭�dcfxdx+lime鈫�鈭�鈭�cefxdx

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