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Maria Isabel Cepeda

Maria Isabel Cepeda. The true measure of an individual is how he treats a person who can do him absolutely no good. —Ann Landers (Respect). [ ( x + 3)^2 – 1] dx. LRAM 2 SUBINTERVALS . Sub intervals from -4 to -3 and -3 to -4 Left part of rectangle is f(-4) and f(-3)

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Maria Isabel Cepeda

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  1. Maria Isabel Cepeda The true measure of an individual is how he treats a person who can do him absolutely no good. —Ann Landers (Respect)

  2. [(x + 3)^2 – 1] dx

  3. LRAM 2 SUBINTERVALS • Sub intervals from -4 to -3 and -3 to -4 • Left part of rectangle isf(-4) and f(-3) • Distance of subintervals is 1: • 1[f(-4) + f(-3)] • 1(0 + – 1) • LRAM: -1u^2

  4. RRAM 2 SUBINTERVALS • Subintervals same as before • Right part of rectangles: f(-3) and f(-2) • Distance still 1 • 1[f(-3) + f(-2)] • 1(-1 + 0) • RRAM: -1u^2

  5. MRAM 2 SUBINTERVALS • Same subintervals • Use midpoints of subintervals • Use f(-3.5) and f(-2.5) • Distance of rectangles still 1 • 1[f(-3.5) + f(-2.5)] • 1(-0.75 + -0.75) • MRAM: -1.5u^2

  6. LRAM 4 SUBINTERVALS • Subintervals from -4 to -3.5, -3.5 to -3, -3 to -2.5, and -2.5 to -2 • Left part of rectangles: f(-4), f(-3.5), f(-3) and f(-2.5) • Distance: 0.5 • 0.5[f(-4) + f(-3.5) + f(-3) + f(-2.5)] • 0.5(0 + -0.75 +-1 + -0.75) • LRAM: 0.5(-2.5) = -1.25U^2

  7. RRAM 4 SUBINTERVALS • Subintervals from -4 to -3.5, -3.5 to -3, -3 to -2.5, and -2.5 to -2 • Right part of rectangles: f(-3.5), f(-3),f(-2.5), and f(-2) • Distance: 0.5 • 0.5[f(-3.5) + f(-3) + f(-2.5) + f(-2)] • 0.5(-0.75 +-1 + -0.75 + 0) • RRAM: 0.5(-2.5) = -1.25U^2

  8. MRAM 4 SUBINTERVALS • Subintervals from -4 to -3.5, -3.5 to -3, -3 to -2.5, and -2.5 to -2 • Middle part of rectangles: f(-3.75), f(-3.25), f(-2.75) and f(-2.25) • Distance: 0.5 • 0.5[f(-3.75) + f(-3.25) + f(-2.75) + f(-2.25)] • 0.5(-0.44 + -0.94 +-0.94 + -0.44) • MRAM: 0.5(-2.76) = -1.38U^2

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