Calculus help please?

Calculus help please?



1. I'm trying to understand what 'dx' is for integral notation, but it's just not making sense! Can someone clarify for me? Why is dx important? What is its purpose? 

2. I'm confused on what ∫ t dx is. What do those signs mean? 

My professor just gave us an assignment and I have gone to her office hours. He was no help and simply told me that it is really simple and I should just look at the book (and I already have). I'm trying really hard not to hate math right now.





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