GATE AG 2013 • Q26
NAT • 1 Mark
Section 1: Engineering Mathematics
Numerical Methods
Subtopic: Numerical solutions of ODEs
Question Statement:
Given $f(x) = e^{-x^2}$ for $x = 1.1, 1.2, 1.3, 1.4, 1.5$, the value of $\int_{1.1}^{1.5} f(x) \, dx$ using Simpson's $1/3$rd rule is ______
Official Answer Key:
0.0761
Step-by-Step Solution & Explanation
f(x) values: f(1.1)=e^(−1.21)=0.29820, f(1.2)=e^(−1.44)=0.23693, f(1.3)=e^(−1.69)=0.18452, f(1.4)=e^(−1.96)=0.14086, f(1.5)=e^(−2.25)=0.10540.
Simpson's 1/3rd rule (h=0.1, 4 intervals): I = (h/3)[f₀+4f₁+2f₂+4f₃+f₄]
= (0.1/3)[0.29820+4(0.23693)+2(0.18452)+4(0.14086)+0.10540]
= (0.03333)[0.29820+0.94772+0.36904+0.56344+0.10540] = (0.03333)(2.2838) = 0.0761.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test