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Math Help: Taking area as a limit


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So i have a quiz tomorrow on finding the area under a curve... I already know 90% of calc 2 from highschool but i am taking it in college to make sure im ready for calc3. The thing is the only thing i didnt learn was summation... specifically the limit of a summation of reimann sums... its 11:47 Pm.. i just need a good guide for the steps to setup and solve the problems... 

 

-_- professor said if i use integration I get a 0 rip

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