How to use the numerical integration of sin calculator
Approximate the integral of sin(x) with the trapezoid rule. Enter lower limit, upper limit, number of trapezoids in the fields above; the trapezoid approximation, exact value, absolute error are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- a — Lower limit
- b — Upper limit
- n — Number of trapezoids
Worked example
With lower limit = 0, upper limit = 3.14159, number of trapezoids = 10, the calculator gives trapezoid approximation ≈ 1.983524; exact value ≈ 2; absolute error ≈ 0.01647643.
Frequently asked questions
What is the formula for the numerical integration of sin calculation?
Trapezoid approximation = trapSin(a,b,n). Exact value = cos(a)-cos(b). Absolute error = abs([Trapezoid approximation]-[Exact value]). Here a is lower limit, b is upper limit, n is number of trapezoids.
What inputs do I need for the numerical integration (trapezoid) of sin(x) calculator?
You need lower limit, upper limit, number of trapezoids. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.