With h = 0.5, the nodes are 0, 0.5 and 1. The composite trapezoidal approximation is $I\approx(h/2)[1+2e^{-0.25}+e^{-1}]=0.73137$. To two decimals this is 0.73. The middle node is weighted twice because it belongs to both trapezoids.
More Numerical methods questions
GATE 2019 MT Q49– Estimate the cube root of 37 using two Newton–Raphson iterations starting with x₀=1. Give…
GATE 2026 MT Q45– Taking the number of intervals as n=3, the value of 00.3e-x2\,dx using the trapezoidal…
GATE 2025 MT Q65– Two consecutive Newton–Raphson estimates of a root of f(x) are x i=8.5 and x i+1=13.5,…
GATE 2022 MT Q37– Which equation fails to converge to a root under Newton–Raphson iteration starting at…
GATE 2022 MT Q61– Estimate the integral of f(x)=0.2+10x2 from 0 to 1 by the single-segment trapezoidal rule:…
GATE 2021 MT Q47– Use Newton–Raphson on f(x)=x- x with initial guess 0.5 radians. The root estimate after…