AP Calculus AB Ch.4 Riemann Sums and Trapezoid …...AP Calculus AB Ch.4 Riemann Sums and Trapezoid...

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AP Calculus AB Ch.4 Riemann Sums and Trapezoid Rule

1. Use a right Riemann sum to approximate ∫ 𝑓(π‘₯)𝑑π‘₯5

1 using 4 equal subintervals.

2. Use a left Riemann sum to approximate ∫ 𝑓(π‘₯)𝑑π‘₯10

βˆ’2 using 4 equal subintervals.

3. Use a midpoint Riemann sum to estimate ∫ 𝑓(π‘₯)𝑑π‘₯10

βˆ’2 using 6 equal subintervals.

4. Use a trapezoidal approximation to estimate ∫ 𝑓(π‘₯)𝑑π‘₯5

0 using 5 equal subintervals.

6. 7. 8.

9. 10. 11.

12.

𝑓(π‘₯) is increasing

𝑓(π‘₯) is decreasing

Left Riemann

Sum

Under Approximation

Over Approximation

Right Riemann

Sum

Over Approximation

Under Approximation

𝑓(π‘₯) is concave DOWN

𝑓(π‘₯) is concave UP

Trapezoid Rule

Under Approximation

Over Approximation

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