How do you use the trapezoidal rule with n=4 to approximate the area between the curve #y=x^2+4x# from 0 to 4?

1 Answer
Oct 26, 2015

Answer:

See the explanation below.

Explanation:

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

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

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

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

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

Now apply the formula (do the arithmetic) for #f(x) = x^2+4x#.

#T_4=(Deltax)/2 [f(x_0)+2f(x_1)+2f(x_2)+ * * * 2f(x_9)+f(x_10)] #