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Approximating Areas with Riemann Sums

AP Calculus AB· difficulty 4/5

Using a right Riemann sum with 4 equal subintervals on [0,4][0, 4] for f(x)=x2f(x) = x^2, the approximation is

  • A

    3030

    check_circle
  • B

    1414

  • C

    2222

  • D

    643\frac{64}{3}

Explanation

Δx=1\Delta x = 1. Right endpoints: 1,2,3,41, 2, 3, 4. Sum of x2x^2 at these: 1+4+9+16=301+4+9+16 = 30. (Exact ∫04x2dx=64/3≈21.3\int_0^4 x^2 dx = 64/3 ≈ 21.3; right sum overestimates increasing function.)

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