Please help, I am stuck...

Question

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Approximation, using the 4 intervals between those given points.

x	4	9	11	14	15
f(x)	-6	-11	-18	-21	-25

Answer 1

The area of a trapezoid is 1/2(x₂ - x₁) (f(x₁) + f(x₂))

Thus, we add the four trapezoids: 1/2(9-4)(-6+-11) + 1/2(11-9)(-11+-18) + 1/2(14-11)(-18+-21) + 1/2(15-14)(-21+-25) = -153