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Trapezoidal Approximation Objective: To find area using trapezoids.

Dec 27, 2015

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  • Trapezoidal ApproximationObjective: To find area using trapezoids.

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

  • Trapezoidal ApproximationAs 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 ApproximationThe area of the first trapezoid is

    The area of the second trapezoid is

    The area of the third trapezoid is

  • Trapezoidal ApproximationThe area of the first trapezoid is

    The area of the second trapezoid is

    This leads us to the following:

  • Sample AP Question

  • Sample AP Question

  • NoteThe AP book made the following notes:DO NOT use your calculators 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 QuestionUsing the subintervals [1,5], [5,8], and [8,10], what is the trapezoidal approximation to

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

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

  • AP QuestionThe expression is the trapezoidal approximation for which of the following definite integrals?

    a) b) c)

    d) e)

  • AP QuestionThe 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 QuestionThe 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 QuestionThe 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 QuestionThe expression is the trapezoidal approximation for which of the following definite integrals?

    a) b) c)

    d) e)

  • AP QuestionThe expression is the trapezoidal approximation for which of the following definite integrals?

    a) b) c)

    d) e)

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