मान ज्ञात कीजिए: int u frac{d^2v}{dx^2} dx - | vedclass

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(A) दोनों समाकलनों के लिए खंडशः समाकलन (Integration by Parts) का उपयोग करने पर: $\int u \frac{d^2v}{dx^2} dx = u \frac{dv}{dx} - \int \frac{du}{dx} \f

Vedclass · Accepted Answer

$u \frac{dv}{dx} - v \frac{du}{dx} + C$

Vedclass · Answer

(A) दोनों समाकलनों के लिए खंडशः समाकलन (Integration by Parts) का उपयोग करने पर: $\int u \frac{d^2v}{dx^2} dx = u \frac{dv}{dx} - \int \frac{du}{dx} \frac{dv}{dx} dx$ $\int v \frac{d^2u}{dx^2} dx = v \frac{du}{dx} - \int \frac{dv}{dx} \frac{du}{dx} dx$ दोनों व्यंजकों को घटाने पर: $\int u \frac{d^2v}{dx^2} dx - \int v \frac{d^2u}{dx^2} dx = (u \frac{dv}{dx} - \int \frac{du}{dx} \frac{dv}{dx} dx) - (v \frac{du}{dx} - \int \frac{dv}{dx} \frac{du}{dx} dx) + C$ $= u \frac{dv}{dx} - v \frac{du}{dx} - \int \frac{du}{dx} \frac{dv}{dx} dx + \int \frac{du}{dx} \frac{dv}{dx} dx + C$ $= u \frac{dv}{dx} - v \frac{du}{dx} + C$

मान ज्ञात कीजिए: $\int u \frac{d^2v}{dx^2} dx - \int v \frac{d^2u}{dx^2} dx$

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