AP Calculus ABmediummcq1 pt

Which of the following definite integrals equals limni=1n2n(2in)2\lim_{n\to\infty}\sum_{i=1}^{n}\frac{2}{n}\left(\frac{2i}{n}\right)^2?

A.02x2dx\int_0^2 x^2\,dx
B.01x2dx\int_0^1 x^2\,dx
C.022x2dx\int_0^2 2x^2\,dx
D.014x2dx\int_0^1 4x^2\,dx

Explanation

Core Concept

Here Δx=2n\Delta x=\frac{2}{n} and the sample points are xi=2inx_i=\frac{2i}{n}, so the integral is 02x2dx\int_0^2 x^2\,dx.

Correct Answer

A02x2dx\int_0^2 x^2\,dx

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