Home/Calculus II/Substitution method/Substitution in definite integralsSection 4.2Substitution in definite integralsWe can return to xxx before evaluating or change the limits directly:Copy LaTeX∫abf(g(x))g′(x) dx=∫g(a)g(b)f(u) du.\int_a^b f(g(x))g'(x)\,dx =\int_{g(a)}^{g(b)}f(u)\,du.∫abf(g(x))g′(x)dx=∫g(a)g(b)f(u)du.View detail →Do not mix limits in xxx with an integrand written in uuu.
We can return to xxx before evaluating or change the limits directly:Copy LaTeX∫abf(g(x))g′(x) dx=∫g(a)g(b)f(u) du.\int_a^b f(g(x))g'(x)\,dx =\int_{g(a)}^{g(b)}f(u)\,du.∫abf(g(x))g′(x)dx=∫g(a)g(b)f(u)du.View detail →