How integrals are convergent? int_(0)^(oo)sin17x dx

remolatg 2020-11-12 Answered
How integrals are convergent?
0sin17xdx
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Expert Answer

Sadie Eaton
Answered 2020-11-13 Author has 104 answers
Step 1
Since there are multiple questions, so we will be answering only the first one.
To deal with such type of Improper Integrals, we will replace the infinity with a variable (usually t), do the integral and then take the limit of the result as t goes to infinity.
We will call these integrals convergent if the associated limit exists and is a finite number (i.e. it’s not plus or minus infinity) and divergent if the associated limit either doesn’t exist or is (plus or minus) infinity.
0sin17xdx=limt0tsin17xdx
limt0tsin17xdx=limt[117(cos(17t)+1)]
=limit does not exist
Thus, 0sin17xdx is not convergent.
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