Integrate int03 (2x3 + 1) dx using Simpson's frac13 rule with n=6. | Numerical Methods 2082

Numerical Methods20825 marksNumerical: Simpson's 1/3 ruleSimpson's 1/3 rule and composite Simpson's 1/3 rule

Integrate $\int_{0}^{3} (2x^3 + 1) dx$ using Simpson's $\frac{1}{3}$ rule with $n=6$ . [5]

Integrate $\int_{0}^{3} (2x^3 + 1) dx$ using Simpson's $\frac{1}{3}$ rule with $n=6$. [5]

$f(x) = 2x^3 + 1$ - Limits: $a = 0$ , $b = 3$ - Number of intervals: $n = 6$ $h = \frac{b-a}{n} = \frac{3-0}{6} = 0.5$ $i$ $xi$ $f(xi) = 2xi^3 + 1$ Coeff Product -------------------------------- 0 0.0 $2(0)+1 = 1.000$ 1 1.000 1 0.5 $2(0.125)+1 = 1.250$ 4 5.000 2 1.0 $2(1)+1 = 3.000$ 2 6.000 3 ...

$f(x) = 2x^3 + 1$ - Limits: $a = 0$, $b = 3$ - Number of intervals: $n = 6$ $$h = \frac{b-a}{n} = \frac{3-0}{6} = 0.5$$ $i$ $xi$ $f(xi) = 2xi^3 + 1$ Coeff Product -------------------------------- 0 0.0 $2(0)+1 = 1.000$ 1 1.000 1 0.5 $2(0.125)+1 = 1.250$ 4 5.000 2 1.0 $2(1)+1 = 3.000$ 2 6.000 3 ...