How to Apply Trapezoidal Rule?

The trapezoidal rule can be applied to solve the definite integral of any given function. It calculates the area under the curve formed by the function by dividing it into trapezoids and is a lesser accurate method in comparison to Simpson’s Rule. Both Simpson’s Rule and Trapezoidal Rule give the approximation value, but Simpson’s Rule results in an even more accurate approximation value of the integrals because Simpson’s Rule uses the quadratic approximation instead of linear approximation.

Follow the below-given steps to apply the trapezoidal rule to find the area under the given curve, y = f(x).

• Step 1: Note down the number of sub-intervals, “n” and intervals “a” and “b”.
• Step 2: Apply the formula to calculate the sub-interval width, h (or) △x = (b – a)/n
• Step 3: Substitute the obtained values in the trapezoidal rule formula to find the approximate area of the given curve,
  ^b∫_a f(x)dx ≈ T_n = (△x/2) [f(x₀) + 2 f(x₁) + 2 f(x₂) +….+ 2 f(_n-1) + f(_n)], where, x_i = a + i△x