Applied Mathematics for Electrical Engineering (3130908)

Question-2c ( ii )-OR

BE | Semester-3 Winter-2019 | 26-11-2019

Q2) (c ( ii ))

Simpson’s $\frac{3}{8} th$ rule

\int_{a}^{b} f (x) d x = \frac{3 h}{8} [(y_{0} + y_{n}) + 2 (y_{3} + y_{6} + . . .) + 3 (y_{1} + y_{2} + y_{4} + . . .)]

; Where,

h = \frac{b - a}{n}

Here,

f (x) = \frac{1}{1 + x}

, and

a = 0; b = 3

Where,

h = \frac{b - a}{n} = \frac{3 - 0}{6} = 0.5

$x$	$0$	$0.5$	$1$	$1.5$	$2$	$2.5$	$3$
$f (x)$	$1$	$0.6667$	$0.5$	$0.4$	$0.3333$	$0.2857$	$0.25$

Simpson’s

\frac{3}{8} th

rule

\int_{a}^{b} f (x) d x = \frac{3 h}{8} [(y_{0} + y_{n}) + 2 (y_{3} + y_{6} + . . .) + 3 (y_{1} + y_{2} + y_{4} + . . .)]

\int_{a}^{b} f (x) d x = \frac{3 (0.5)}{8} [(1 + 0.25) + 2 (0.4) + 3 (0.6667 + 0.5 + 0.3333 + 0.2857)]

\int_{a}^{b} f (x) d x = 1.3888