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

What is Leibniz's rule for differentiating an integral with variable limits $\frac{d}{dx} \int_{u(x)}^{v(x)} f(t)\,dt$?

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

정답

$\frac{d}{dx} \int_{u(x)}^{v(x)} f(t)\,dt = f(v(x)) \cdot v'(x) - f(u(x)) \cdot u'(x)$.

해설

Widely tested in JEE Main calculus questions involving limits of the form $\frac{0}{0}$ evaluated using L'Hôpital's Rule.

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