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What is King's Property of definite integrals for $\int_a^b f(x)\,dx$?

Lernkarte aus dem Deck JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry.

Antwort

$\int_a^b f(x)\,dx = \int_a^b f(a + b - x)\,dx$. In particular, $\int_0^a f(x)\,dx = \int_0^a f(a - x)\,dx$.

Erklärung

Adding the original integral $I$ to the transformed integral often eliminates transcendental or trigonometric denominators.

Synthetischer Inhalt · Redaktion: Ada