How do you approximate of #int sinx(dx)# from #[0,pi]# by the trapezoidal approximation using n=10?

1 Answer
Oct 15, 2015

Answer:

See the explanation section.

Explanation:

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

In this question we have:
#f(x) = sinx#
#{a,b] = [0, pi]#, and
#n=10#.

So we get
#Delta x = (b-a)/n = (pi-0)/10 = pi/10#

The endpoints of the subintervals are found by beginning at #a=0# and successively adding #Delta x = pi/10# to find the points until we get to #x_n = b = pi#.

#x_0 = 0#, #x_1 = pi/10#, #x_2 = (2pi)/10#, #x_3 = (3pi)/10# . . . #x_9 = (9pi)/10#, and #x_10 = (10pi)/10 = 10 = b#

Now apply the formula (do the arithmetic) for #f(x) = sinx#.

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