Campus Livre
changeIntegrationVariable
Substitutes a new variable into an integral.
Category: Mathematics > Calculus
Syntax
G = changeIntegrationVariable(F, old, new)Rewrites the integral F by setting old equal to the expression new of a new variable.
Description
The substitution x = g(u) turns int(f(x), x, a, b) into int(f(g(u))*g'(u), u, ua, ub), where the new limits solve g(u) = a and g(u) = b. The function does exactly this bookkeeping, which is easy to get wrong by hand. F must be an int expression, so an abstract integrand such as f(x) is the clearest way to see the effect.
Input arguments
F- Unevaluated integral created with
int. old- The integration variable of
F. new- Expression of the new variable, such as
sqrt(z).
Output arguments
G- Integral in the new variable, with the integrand multiplied by the derivative of the substitution and the limits transformed.
Example
Substitute x = sqrt(z)
syms x u
F = int(2*x*exp(x^2), x, 0, 1);
G = changeIntegrationVariable(F, x, sqrt(u))Output
G = int(exp(u), u, 0, 1)