Let . Using equal subintervals on and right endpoints, express as , and simplify the…

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let g(x)=x2+2xg(x)=x^{2}+2x. Using NN equal subintervals on [0,2][0,2] and right endpoints, express ∫02g(x) dx\displaystyle \int_{0}^{2} g(x)\,dx as lim⁡N→∞∑i=1N( ⋅ )\displaystyle \lim_{N\to\infty}\sum_{i=1}^{N}(\,\cdot\,), and simplify the summand completely so that it contains only ii and NN (no xx).

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