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L’intégrale vaut 0.
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To solve the integral
we start by using the property of cosine, which states that
. Here, we can set
and
.
Using this identity, we can rewrite the cosine function:
Since
, we substitute this into our equation:
Thus, the integral becomes:
We can factor out
:
Now, we need to evaluate the two integrals separately.
-
Integral of
:
The integral ofis : Evaluating it fromto : -
Integral of
:
The integral of is :Evaluating from to :
Putting it all together, we substitute back into our original expression:
Thus, the value of the integral is