MATLAB offset when plotting integration of sin -


i have question, because work many functions, have trouble when trying plot integral of sine (i using matlab 2010):

clear close clc  x = linspace(-10, 10, 100);  f = @(x) sin(x);  = arrayfun(@(x) quad(f, 0, x), x); plot(x, f(x),'r', x, i, 'b')

i expect having -cos(x), instead offset of 1, why happening? how should fix problem?

the fundamental theorem of calculus says indefinite integral of nice function f(x) equal function's antiderivative f(x), unique up-to additive constant. further, definite integral has form:

fundamental theorem of calculus

in form, constant of integration cancel out, , integral equal desired antiderivative only if lower bound evaluation vanishes. however, -cos(0) not vanish , has value of -1. in order calculate desired antiderivative f(x), lower bound evaluation should added right-hand side.

plot(x, f(x),'r', x, i+ (-cos(0)), 'b');

this equivalent of assigning initial value solution of odes la ode45.


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