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49

Step-by-step Answer
PAGE: 552SET: ExercisesPROBLEM: 49
Please look in your text book for this problem Statement

The integral is .

Rewrite the integral as 

Consider the second integral on right side .

Now apply comparison value theorem for above integral.

Consider the fact  and it implies that  .

Comparison theorem:

Suppose that  and are continuous functions with  for ,

1. If  is convergent, then  is convergent.

2.If  is divergent, then  is also divergent.

Here  and 

Since  is a finite value, it is convergent.

By comparison theorem,  is convergent.

 is convergent, it follows that  is also convergent.

 and are convergent, thenimage is convergent.

is convergent.



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