Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain why or give an example that disproves thestatement. If ∫a∞f(x) dx and ∫a∞ g(x) dx are both convergent, then ∫a∞ [f(x)  + g(x)] dx  is convergent.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 35E
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Determine whether the statement is true or false. If it is true, explain
why. If it is false, explain why or give an example that disproves the
statement.

If ∫af(x) dx and ∫a g(x) dx are both convergent, then ∫a [f(x)  + g(x)] dx  is convergent.

Expert Solution
Step 1

Given:  af(x)dx and ag(x)dx are convergent.

To Show: af(x)+g(x) dx is convergent.

 

We know,au(x)dx is convergent if limtatu(x)dx=Li ; LiR.

Implies

limtatf(x)dx=L1 ; L1R

limtatg(x)dx=L2 ; L1R

 

 

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