calculus

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The function f is continuous on the closed interval [0,6] and has values that are given in the table below.

x |0|2|4|6
f(x)|4|K|8|12

The trapezoidal approximation for(the integral):

6
S f(x) dx
1

found with 3 subintervals of equal length is 52. What is the value of K?

How do you do this with the formula

b-a/(2n) * f(x0) + 2(fx1) + f(xn)?

• calculus -

The formula for the area of a trapezoid is 1/2(b_1 + b_2)h where h = delta (x)

Therefore, A = 1/2(4+k)2 + 1/2(k+8)2 + 1/2(8+12)2 = 54

Solving that equation yields k = 10.

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