Question

Difference between simpsons and trapezoidal rule

Answer 1

Simpson's rule and the Trapezoidal rule are approximations of the definite integral of a function. If the definite integral 《 b{a f(x) 》 has to be determined, the expression to approximate the value of the integral is given by the two rules as follows:

Simpson's rule:  b{a f(x) =
$( \frac{b - a}{6} )(f(a) + 4 \times f( \frac{a + b}{2} ) + f(b))$
Trapezoidal rule: b{a f(x) =
$(b - a) \times \frac{f(a) + f(b)}{2}$
The Trapezoidal rule determines the area under the graph by approximating it to that of a trapezoid. Simpson's rule approximates the area to that under a quadratic polynomial. This makes it a more complex method and one that yields a value closer to the definite integral that is actually being determined.

${ -- it is the sign of integration$

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