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홈 / 라이브러리 / JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry / AI 플래시카드

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

덱 'JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry'의 플래시카드.

정답

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

해설

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

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