[DOCS] Update examples to use new interface #224
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Most of the examples were on the old interface, but people were confused about the deprecation warnings and lack of documentation about the new interface. This pr addresses the lack of examples and tries to motivate the interfaces by expanding the FAQ. Remarkably, there are lots of questions about integration on discourse and slack, so we should pay more attention to updating the FAQ. Also, if we can add docstrings to the web documentation for
(Batch)IntegralFunctioneither here or in SciML/SciMLBase.jl#609 then we could address #218