2) Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of (10)∫(1) f(x)dx

Question

x 1 3 4 6 7 9 10
f(x) 4 8 6 10 10 12 16

Answer 1

you have the values. Just compute the area of the kth trapezoid using
a_k = (f(x_k)+f(x_k+1))/2 * (x_k+1-x_k) for k=1..6

For example, a₁ = (4+8)/2 * (3-1) = 12