Question

can someone explain to me how the sum and integral notations are related ?

Answer 1

look up Reimann Sum

Answer 2

is the summation , the approximation of the integral ? or the integral , the approximation of the sum ?

Answer 3

well the integral sign and summation sign both signify the same thing
so they are the sum of something
in basic terms in integral, it is the sum of the derivative (limit -> 0) of a function from one bound to another and the the corresponding integral is the area under the curve
in reimann sum, it is basically the same thing but with respect to approximations

Answer 4

http://tutorial.math.lamar.edu/Classes/CalcI/AreaProblem.aspx

Answer 5

roughly speaking $$\large \sum_{i=1}^{n} f(x_i) \Delta x \approx \int_{a}^{b} f(x) dx$$ you can think of the integral as the limiting case , when \( \Delta x \) is infinitesimally small

Answer 6

we approximate the area under the curve with rectangles, and add up their total area