Find following integral using composite trapezoidal rule using 2 segme | Numerical Methods 0

Numerical Methods05 marksNumerical: Composite trapezoidal ruleTrapezoidal rule and composite trapezoidal rule

Find following integral using composite trapezoidal rule using 2 segments (k=2) and 4 segments (k=4). $\int_{2}^{8} (x+3)^2 dx$ [5]

Find following integral using composite trapezoidal rule using 2 segments (k=2) and 4 segments (k=4). $$\int_{2}^{8} (x+3)^2 dx$$ [5]

Integral: $\displaystyle\int2^8 (x+3)^2\,dx$ - Lower limit: $a = 2$ - Upper limit: $b = 8$ - Integrand: $f(x) = (x+3)^2$ - Cases: $k = 2$ segments and $k = 4$ segments All data present. $$\inta^b f(x),dx \approx \frac{h}{2}\left[f(x0) + 2\sum{i=1}^{k-1}f(xi) + f(xk)\right], \quad h = \frac{b-a}{...

Integral: $\displaystyle\int2^8 (x+3)^2,dx$ - Lower limit: $a = 2$ - Upper limit: $b = 8$ - Integrand: $f(x) = (x+3)^2$ - Cases: $k = 2$ segments and $k = 4$ segments All data present. $$\inta^b f(x),dx \approx \frac{h}{2}\left[f(x0) + 2\sum{i=1}^{k-1}f(xi) + f(xk)\right], \quad h = \frac{b-a}{...

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