How do you Use the trapezoidal rule with #n=10# to approximate the integral #int_0^2sqrt(x)*e^(-x)dx#?

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Answer 1 · 2014-11-14T23:28:26

Let #f(x)=sqrt{x}e^{-x}=sqrt{x}/e^x#.

#Delta x={b-a}/n={2-0}/10=0.2#

By summing up the areas of trapezoids shown below,

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we have

#T_{10}=[f(0)+2f(0.2)+2f(0.4)+cdots+2f(1.8)+f(2)]{Delta x}/2approx 0.64#

I hope that this was helpful.