Question

If three equal subdivisions of [-4, 2] are used, find the trapezoidal approximation of integral of (e^(-x))/2 dx from -4 to 2.

Answer 1

Trapezoidal rule:
$\int\limits^b_a {f(x)} \, dx=(b-a)* \frac{f(a)+f(b)}{2}$
... = $(2+4)* \frac{e ^{4} +e ^{-2} }{4}$
= $6* \frac{e ^{4} + \frac{1}{e ^{2} } }{4}$
= $\frac{3(e ^{6}+1) }{2e^{2} }$