# Homework Solution: For trapezoid and Simpson methods, the numerical integration I=int_{0}^{1}sqrt{1-x^2}dx h…

For trapezoid and Simpson methods, the numerical integration have relative error where is the numerical result using intervals between [0, 1]. (i) Explain the power-law scaling with an exponent 1.5 (instead of 2 and 4 as expected for the trapezoid and Simpson's method, respectively). (ii) How can one circumvent this problem and restore the desired error scaling ?

power law scaling:

Ce trapezoid and Simpson courses, the numerical integration have not-absolute fault where is the numerical upshot using intervals among [0, 1].

(i) Explain the power-principle scaling with an propounder 1.5 (instead of 2 and 4 as expected ce the trapezoid and Simpson’s course, respectively).

(ii) How can single outwit this completion and reinstate the desired fault scaling ?

## Expert Counter-argument

power principle scaling:

power principle scaling is a scaling with a fixed which simpliy
multiplies the originalpower principle proportion with a
constant. ii) ce trapeziod ERROR SCALING

I=0.2