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Trapezoidal Rule

Trapezoidal Rule. What is the formula for a trapezoid?. How do you find the area of the following trapezoid? A = + h How can we use this rule to help us find the area under a curve? . h. What is the Trapezoidal Rule? .

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Trapezoidal Rule

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  1. Trapezoidal Rule

  2. What is the formula for a trapezoid? • How do you find the area of the following trapezoid? • A = +h • How can we use this rule to help us find the area under a curve? h

  3. What is the Trapezoidal Rule? • Let’s find the area of a function f(x) from a to b. Recall that is the area under the curve from a to b. We will begin by dividing the region into 4 equal pieces. The width of each piece will be ∆x where Next, we will find the area of each of the four trapezoids and sum them up.

  4. A = +h • Trap #1 = f(a) + f( • Trap #2 = f( • Trap #3 = f( • Trap #4 = f( To approximate the area from a to b, we need to add up these four pieces = f(a)+ f( +f(f( + f( Notice we can factor out ½ and and get [f(a) + f( +f(f( + f( Which can be further simplified to say: [f(a) + 2f( +] *****(We will let f(a) = ) Finally we can see the Trapezoidal Rule: +

  5. Example #1 • How can you find the area under the curve from 0 to 4 of the function +1 that has 4 sections? + [f( = 6.75

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