How do you use the trapezoidal rule to approximate the Integral from 0 to 0.5 of #(1-x^2)^0.5 dx# with n=4 intervals?

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Answer 1 · 2015-10-06T16:24:08

See the explanation section, below.

On #[a,b]=[0, 0.5]#, with #n=4#, we get

#Delta x = (b-a)/n = (0.5-0)/4 = 0.125#

The endpoints of the subintervals are found by beginning at #a=0# and successively adding #Delta x# to find the points.

#x_0 = 0#, #x_1 = 0.125#, #x_2 = 0.250#, #x_3 = 0.375#,, #x_4 = 0.5#

Now apply the formula (do the arithmetic):

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