Can we simplify the integral of a dot product to just the product itself?

[fredrogers3]

Hello, I have a quick question about integrals of dot products. We are learning about magnetic flux as the integral of b dot da. However, what circumstances must be present where we can simplify this integral into (b*a) and ignore the integral?

 

[Simon Bridge]

You already know the answer:
You know how a scalar product works for vectors right? This is the same thing.
Consider your question in two parts ... you want to know when $$\vec{B}\cdot d\vec{A}=BdA$$ and, at the same time, $$\int_A B.dA = BA$$ ...