Solved – Civil GATE 2021, Set1, Q.27 – The Value of ∫𝒆x𝒅𝒙 using the Trapezoidal Rule

Problem Statement:

The value of ₀¹∫𝒆^𝒙𝒅𝒙 using the trapezoidal rule with four equal subintervals

is____

Solution: (B)

Also Check: Solution of GATE 2021, CE, Set1 (Q.1 to Q.100)

The equal interval, dx = (b-a)/n = (1 – 0)/4 = 0.25

Area using the Trapezoidal Rule, A = dx/2 *[f(x₀) + 2f(x₁) + 2f(x₂) + … + 2f(x_n-1) + f(x_n)]

f(x) = e^x

Hence, A = 0.25/2 * [e⁰ + 2*e^0.25 + 2e^0.50 + 2e^0.75 + e¹]

A = 0.125*[1 + 2.568 + 3.297 + 4.234 + 2.718]

A = 1.727