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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 -,, then for any real number c,

-fxdx=___+___

Short Answer

Expert verified

limd-dcfxdx+limecefxdx

Step by step solution

01

Step 1. Given information.

Consider the given integral,

-fxdx

02

Step 2. Defining improper integrals.

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

-fxdx=-cfxdx+cfxdx=limd-dcfxdx+limecefxdx

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