Discrete vs. Continuous

Calculus Level 2

x=1n(ax+b)0n(ax+b)dx=?\large \sum_{x=1}^n (ax+b) - \int_0^n (ax+b) \, dx = ?

Hint: There is a nice geometric interpretation of this that doesn't require any calculus, as long as you understand that the definite integral represents the area between the xx-axis and the function between x=0x=0 and x=nx=n.

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