Numerical Method20805 marksNumerical: Composite trapezoidal rule integrationMulti-Segment Trapezoidal rule
Find the following integral using composite trapezoidal rule for using 2 segments (k=2) and 4 segments (k=4).
Find the following integral using composite trapezoidal rule for using 2 segments (k=2) and 4 segments (k=4). $$\int_{2}^{4} (x^3 + 2) dx$$ [5]
- Integrand: $f(x) = x^3 + 2$ - Lower limit: $a = 2$ - Upper limit: $b = 4$ - Segment counts: $k = 2$ and $k = 4$ Formula: $$I \approx \frac{h}{2}\left[f(x0) + 2\sum{i=1}^{k-1}f(xi) + f(xk)\right], \quad h = \frac{b-a}{k}$$ $$\int2^4 (x^3+2),dx = \left[\frac{x^4}{4}+2x\right]2^4 = (64+8)-(4+4) =...