How do you use the Trapezoidal Rule with step size n=4 to estimate #int t^3 +t) dx# with [0,2]?

1 Answer
Nov 17, 2015

Answer:

Assuming that the variables should match see below.

Explanation:

Approximate the Integral #int_a^b f(x) dx# using trapezoidal approximation with #n# intervals.

In this question we have:
#f(x) = x^3+x#
#{a,b] = [0, 2]#, and
#n=4#.

So we get
#Delta x = (b-a)/n = (2-0)/4 = 1/2#

The endpoints of the subintervals are found by beginning at #a=0# and successively adding #Delta x = 1/2# to find the points until we get to #x_n = b = 4#.

#x_0 = 0#, #x_1 = 1/2#, #x_2 =2/2 = 1#, #x_3 = 3/2# and #x_4 = 4/2 = 2 = b#

Now apply the formula (do the arithmetic) for #f(x) = x^3+x#.

#T_4=1/2Deltax [f(x_0)+2f(x_1)+2f(x_2)+2f(x_3) + f(x_4)] #