Consider the below data:
The value of by Trapezoidal rule will be:

Question

Question

This question was previously asked in

AAI ATC Junior Executive 2018 Official Paper (Shift 1)

Answer 1

Concept:

Trapezoidal rule states that for a function y = f(x)

x	x0	x1	x2	x3	……	xn
y	y0	y1	y2	y3	……	yn

xn = x0 + nh, where n = Number of sub-intervals

h = step-size

---(1)

For a trapezoidal rule, a number of sub-intervals must be a multiple of 1.

Calculation:

Here: x₀ = 4, x₁ = 3, x₂ = 12, h = 1

From equation (1);

Key Points:

Apart from the trapezoidal rule, other numerical integration methods are:

Simpson’s one-third rule:

For applying this rule, the number of subintervals must be a multiple of 2.

..2)

Simpson’s three-eighths rule:

For applying this rule, the number of subintervals must be a multiple of 3.