Calculus

The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Sum Approximation, using the intervals between those given points.
x 10;12;15;19;20
f(x) -2;-5;-9;-12;-16

A) -8.750
B) -7.000
C) -8.400
D) -5.500

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  1. DRAW IT !!
    get area of trapezoids
    (12-10)(-5-2)/2+(15-12)(-9-5)/2+(19-15)(-12-9)/2+(20-19)(-15-12)/2
    divide by the length to get average height
    20-10 = 10 is length

    (2)(-7)/2 + (3)(-14)/2 + ...

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  2. Using the trapezoidal rule, the area A is approximated by
    4
    ∑(xk+1-xk)*(f(xk+1)+f(xk))/2
    k=1

    = 2(-7/2) + 3(-7) + 4(-21/2) + 1(-14) = -84

    The average value is A/(20-10) = -8.4

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