Free calculator

Numerical Methods — Root Finding & Numerical Integration

Find roots by bisection or Newton's method, and approximate definite integrals by the trapezoidal or Simpson's rules. Type f(x) with ordinary JavaScript math — use x as the variable and Math.* functions, for example x*x*x - 2*x - 5 or Math.sin(x) - x/2.

Bisection: f(a)·f(b) < 0 ⇒ halve (a, b) each step

Newton: x_n+1 = x_n − f(x_n)/f′(x_n)

Trapezoidal: ∫_a^b f ≈ (h/2)(f₀ + 2Σf_i + f_n) Simpson: ∫_a^b f ≈ (h/3)(f₀ + 4Σf_odd + 2Σf_even + f_n), n even

h = (b − a)/n	panel width for n subintervals
f′(x)	estimated here by a central finite difference, so you only enter f(x)

Root finding

f(x) Method Bracket a Bracket b Initial guess x₀ Tolerance Max iterations

Numerical integration

f(x) Lower limit a Upper limit b Subintervals n Method

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.