Tabulated x values are 1,3,5,15,25 with corresponding f(x) values 6,8,10,12,5. Use Simpson’s 1/3 rule to evaluate $\int_1^{25}f(x)dx$, rounded to one decimal place.
The data have two equal-spacing blocks, so apply Simpson separately on [1,5] with h = 2 and on [5,25] with h = 10. The first gives $I_1=(2/3)[6+4(8)+10]=32$. The second gives $I_2=(10/3)[10+4(12)+5]=210$. Total integral is 32 + 210 = 242.0. Applying one uniform spacing across all five unequal-spaced nodes would be invalid.
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