The value of the integral \[ \int_{0.2}^{1.4} (\sin x - \log_e x + e^x) \, dx \] using Simpson's three-eighth rule, by taking interval size \( h = 0.2 \), is:
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Simpson’s three-eighth rule is a numerical integration technique that is particularly effective when dealing with irregular intervals and provides better accuracy for certain functions
Simpson's three-eighth rule uses given function values at specified intervals to calculate a weighted sum, yielding an approximate integral of 4.052985.