GATE (TF) Textile 2014 Question Paper Solution | GATE/2014/TF/30

Question 30 (Textile Engineering & Fibre Science)

$\int_{0}^{2}e^xdx$ is evaluated both by Trapezoidal rule and Simpson’s $\frac {1}{3}$ rule by taking two subintervals. The difference between the results, accurate to the second decimal place, is ……

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$\int_{0}^{2}e^xdx$
Here, h=2-0/2=1

	y(0)	y(1)	y(2)
x	0	1	2
y	1	2.718	7.389

Now, By Trapezoidal rule-
f(x)= $\frac{h}{2}[(y(0)+y(2))+y(1)]$
f(x)= $\frac{1}{2}[(1+7.389)+2\times 2.718]$
f(x)=6.912

Now, Simpson’s $\frac {1}{3}$ –
{f}'(x)= $\frac{h}{3}[(y(0)+y(2))+2\times o+4\times y(1)]$
{f}'(x)= $\frac{1}{3}[(1+7.389)+0+4\times 2.718]$
{f}'(x)=6.4203

Difference between the values=f(x)-{f}'(x)
=6.912-6.4203
=0.49 (Ans)

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