How do you Use the trapezoidal rule with #n=10# to approximate the integral #int_1^2ln(x)/(1+x)dx#?
1 Answer
The trapezoidal rule is:

First, we need to find our different values of x: since
#1<=x<=2# and we need to split up our function into ten parts. So, quite simply, the values of x we need are 1, 1.1, 1.2, ..., 1.9, 2, with#x_1=1# ,#x_2=1.1# , and so on. 
Next, we need to substitute the values of
#a# and#b# , which are 1 and 2 respectively, into the equation. Also plug in#n=10# .
#int_1^2ln(x)/(1+x)dx ~~ (21)/(2*10)*(f(x_1)+2f(x_2)+...+2f(x_10)+f(x_(11)))# 
Next, we evaluate
#f(x_1)# ,#f(x_2)# and so on. As an example:
#f(x_1) = f(1) = ln(1)/(1+1) = ln(1)/2 = 0#
#f(x_2) = f(1.1) = ln(1.1)/(1+1.1) = ln(1.1)/2.1 ~~ 0.04539# 
Finally, we plug all these values into our equation.
#int_1^2ln(x)/(1+x)dx ~~ (21)/(2*10)*(f(1)+2f(1.1)+...)#
This should provide an approximate answer to any integral.