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

デッキ「JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry」の単語カード。

解答

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

解説

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

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