Trapezoidal Rule Calculator: What It Calculates

Trapezoidal Rule Calculator focuses on a specific mathematical operation or relationship. The output depends on the values, expression, and conventions used in the calculation.

The Formula or Method

The trapezoidal rule approximates an integral using trapezoids: ∫_a^b f(x)dx ≈ h/2[f(x0)+2Σf(xi)+f(xn)] for equally spaced points.

Sanity check

Estimate the size and sign of the answer before accepting the displayed result. A quick mental check can catch an incorrect input or copied expression.

Using Trapezoidal Rule Calculator

Enter the required numbers or mathematical expression carefully. For formulas involving multiple variables, keep parentheses and signs exactly as intended.

1. Identify the variables or values used by the formula.
2. Enter them with the correct signs and order.
3. Calculate the result.
4. Substitute the answer back into the relationship when a verification is practical.

Worked Example

For one interval of width 2 with endpoint values 3 and 5, the trapezoidal estimate is 8.

Checking the Result

Rounding can slightly change the displayed answer, especially with irrational numbers, logarithms, numerical integration, or repeated operations. Use additional precision when the final result requires it.