 # Trapezoidal Approximation Objective: To find area using trapezoids.

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Trapezoidal Approximation Objective: To find area using trapezoids.

Trapezoidal Approximation We will now approximate the area under a curve by using trapezoids rather than rectangles. This is only an approximation; we will never take the limit to find the exact area.

Trapezoidal Approximation As we did before, we will draw vertical lines to divide the interval into n subintervals. This time, we will construct n trapezoids.

Trapezoidal Approximation As we did before, we will draw vertical lines to divide the interval into n subintervals. This time, we will construct n trapezoids. The area of a trapezoid is. The height of the each trapezoid is what we called before.

Trapezoidal Approximation The area of the first trapezoid is The area of the second trapezoid is The area of the third trapezoid is

Trapezoidal Approximation The area of the first trapezoid is The area of the second trapezoid is This leads us to the following:

Sample AP Question

Note The AP book made the following notes: DO NOT use your calculator’s statistics regression equation to find f(x) and then the Fundamental Theorem of Calculus; this may give you a more accurate answer (D) but it is not what you were asked for. The left hand sum is (E) and the right hand sum is (A).

AP Question Using the subintervals [1,5], [5,8], and [8,10], what is the trapezoidal approximation to

AP Question Using the subintervals [1,5], [5,8], and [8,10], what is the trapezoidal approximation to

AP Question Using the subintervals [1,5], [5,8], and [8,10], what is the trapezoidal approximation to

AP Question The expression is the trapezoidal approximation for which of the following definite integrals? a) b) c) d) e)

AP Question The expression is the trapezoidal approximation for which of the following definite integrals? There are 4 trapezoids (why), so n = 4. We know that and if n = 4 it becomes so b – a = 2. Our only two choices are A and D.

AP Question The expression is the trapezoidal approximation for which of the following definite integrals? There are 4 trapezoids (why), so n = 4. We know that and if n = 4 it becomes so b – a = 2. Our only two choices are A and D. If a = 0, the bases are f(0), f(1/2), f(1), f(3/2), f(2). If a = 1, the bases are f(1), f(3/2), f(2), f(5/2), f(3).

AP Question The expression is the trapezoidal approximation for which of the following definite integrals? There are 4 trapezoids (why), so n = 4. We know that and if n = 4 it becomes so b – a = 2. Our only two choices are A and D. If a = 0, the bases are f(0), f(1/2), f(1), f(3/2), f(2). If a = 1, the bases are f(1), f(3/2), f(2), f(5/2), f(3).

AP Question The expression is the trapezoidal approximation for which of the following definite integrals? a) b) c) d) e)

AP Question The expression is the trapezoidal approximation for which of the following definite integrals? a) b) c) d) e)