Solve the double integration using Simpson's 1/3 rule. | Numerical Methods 2080

Numerical Methods20805 marksNumerical: Double integration Simpson's ruleDouble integration using Simpson's rules

Solve the double integration using Simpson's 1/3 rule. $\int_{2}^{2.6} \int_{4}^{4.4} \frac{dxdy}{xy}$ [5]

Solve the double integration using Simpson's 1/3 rule. $$\int_{2}^{2.6} \int_{4}^{4.4} \frac{dxdy}{xy}$$ [5]

$I = \int{2}^{2.6} \int{4}^{4.4} \frac{dx\,dy}{xy}$ - Inner variable $x$ : limits $4$ to $4.4$ - Outer variable $y$ : limits $2$ to $2.6$ - Integrand: $f(x,y) = \dfrac{1}{xy}$ Using $n = 2$ subintervals in each direction: - $h = \dfrac{4.4 - 4}{2} = 0.2$ , giving $x0=4.0,\ x1=4.2,\ x2=4.4$ -

$$I = \int{2}^{2.6} \int{4}^{4.4} \frac{dx,dy}{xy}$$ - Inner variable $x$: limits $4$ to $4.4$ - Outer variable $y$: limits $2$ to $2.6$ - Integrand: $f(x,y) = \dfrac{1}{xy}$ Using $n = 2$ subintervals in each direction: - $h = \dfrac{4.4 - 4}{2} = 0.2$, giving $x0=4.0,\ x1=4.2,\ x2=4.4$ -

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