Project ForgeEngineering Mathematics
Numerical Methods
GATE 2013
Medium
The value of the integral ∫[0.1 to 0.5] e^(−x³) dx evaluated by Simpson's rule using 4 subintervals, up to 3 digits after the decimal point, is _____
0.385(± 0.01 accepted)
Explanation
h=(0.5−0.1)/4=0.1; nodes x=0.1,0.2,0.3,0.4,0.5 give f=0.99900, 0.99203, 0.97336, 0.93801, 0.88250. Simpson's rule: (h/3)[f0+4f1+2f2+4f3+f4]=(0.1/3)[0.99900+3.96813+1.94672+3.75202+0.88250]=(0.03333)(11.5484)≈0.385.
Source: GATE CH 2013 (2013)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.