ap calculus ab ch.4 riemann sums and trapezoid …...ap calculus ab ch.4 riemann sums and trapezoid...

AP Calculus AB Ch.4 Riemann Sums and Trapezoid Rule 1. Use a right Riemann sum to approximate ∫ () 5 1 using 4 equal subintervals. 2. Use a left Riemann sum to approximate ∫ () 10 −2 using 4 equal subintervals.

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AP Calculus AB Ch.4 Riemann Sums and Trapezoid Rule

1. Use a right Riemann sum to approximate ∫ 𝑓(𝑥)𝑑𝑥5

1 using 4 equal subintervals.

2. Use a left Riemann sum to approximate ∫ 𝑓(𝑥)𝑑𝑥10

−2 using 4 equal subintervals.

Page 2: AP Calculus AB Ch.4 Riemann Sums and Trapezoid …...AP Calculus AB Ch.4 Riemann Sums and Trapezoid Rule 1. Use a right Riemann sum to approximate ∫𝑓(𝑥)𝑑𝑥 5 1 using 4

3. Use a midpoint Riemann sum to estimate ∫ 𝑓(𝑥)𝑑𝑥10

−2 using 6 equal subintervals.

4. Use a trapezoidal approximation to estimate ∫ 𝑓(𝑥)𝑑𝑥5

0 using 5 equal subintervals.

Page 3: AP Calculus AB Ch.4 Riemann Sums and Trapezoid …...AP Calculus AB Ch.4 Riemann Sums and Trapezoid Rule 1. Use a right Riemann sum to approximate ∫𝑓(𝑥)𝑑𝑥 5 1 using 4

6. 7. 8.

Page 4: AP Calculus AB Ch.4 Riemann Sums and Trapezoid …...AP Calculus AB Ch.4 Riemann Sums and Trapezoid Rule 1. Use a right Riemann sum to approximate ∫𝑓(𝑥)𝑑𝑥 5 1 using 4

9. 10. 11.

Page 5: AP Calculus AB Ch.4 Riemann Sums and Trapezoid …...AP Calculus AB Ch.4 Riemann Sums and Trapezoid Rule 1. Use a right Riemann sum to approximate ∫𝑓(𝑥)𝑑𝑥 5 1 using 4

12.

𝑓(𝑥) is increasing

𝑓(𝑥) is decreasing

Left Riemann

Sum

Under Approximation

Over Approximation

Right Riemann

Sum

Over Approximation

Under Approximation

𝑓(𝑥) is concave DOWN

𝑓(𝑥) is concave UP

Trapezoid Rule

Under Approximation

Over Approximation

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