The integral of [tex]\int\limits {12cos(4\theta )}\ is\ 3sin4\theta +C[/tex]
Integration is a way of adding parts to find the whole. Integration can be used to find areas, volumes, central points and many useful things.
[tex]\int\limits {12cos(4\theta )} \, d\theta\\\\ =12\int\limits {cos(4\theta )} \, d\theta\\\\=12(\frac{sin4\theta}{4}) +C\\\\=3sin4\theta +C[/tex]
Where C is the constant of integration
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