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Chapter 7: Q.1.a) (page 630)

If 0鈮�f(x)鈮�g(x)for every x鈮�0 and the improper integral鈭�0鈭�g(x)dxconverges, then the improper integral 鈭�0鈭�f(x)dxconverges. The objective is to whether determine the statement is true or false

Short Answer

Expert verified

True

Step by step solution

01

To determine given statement is true or false 

The improper integral鈭�0鈭�g(x)dxis convergent .Therefore ,

鈭�0鈭�g(x)dx=A,where A is finite.

Given that 0鈮�f(x)鈮�g(x).

Therefore,0鈮�鈭�0鈭�f(x)dx鈮�鈭�0鈭�g(x)dx

鈭�0鈭�f(x)dx鈮�A.

Therefore, the improper integral鈭�0鈭�f(x)dxconverges.

Therefore ,the given statement is true.

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