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Approximating Areas with Riemann Sums

AP Calculus AB· difficulty 3/5

Estimate ∫04x2 dx\int_0^4 x^2\,dx using a <strong>left</strong> Riemann sum with 4 equal subintervals.

  • A

    2222

  • B

    1010

  • C

    3030

  • D

    1414

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Explanation

Subintervals [0,1],[1,2],[2,3],[3,4][0,1],[1,2],[2,3],[3,4], left endpoints 0,1,2,30, 1, 2, 3. Sum: 1⋅(0+1+4+9)=141 \cdot (0 + 1 + 4 + 9) = 14.

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