Mathematics · essential
Property under substitution in definite integrals for JEE
The fundamental theorem of calculus, properties of definite integrals
Formula
\[\int_a^b f(g(x))g'(x)\,dx=\int_{g(a)}^{g(b)} f(t)\,dt\]
Variables: \(t=g(x)\).
Conditions: Valid when substitution is differentiable and monotone or otherwise legitimate.
Definite integral evaluation by substitution.