કિંમત શોધો: int u frac{d^2v}{dx^2} dx - int v | vedclass

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Question

(A) બંને સંકલન માટે ખંડશઃ સંકલન (Integration by Parts) નો ઉપયોગ કરતા: $\int u \frac{d^2v}{dx^2} dx = u \frac{dv}{dx} - \int \frac{du}{dx} \frac{dv}{dx

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) બંને સંકલન માટે ખંડશઃ સંકલન (Integration by Parts) નો ઉપયોગ કરતા: $\int u \frac{d^2v}{dx^2} dx = u \frac{dv}{dx} - \int \frac{du}{dx} \frac{dv}{dx} dx$ $\int v \frac{d^2u}{dx^2} dx = v \frac{du}{dx} - \int \frac{dv}{dx} \frac{du}{dx} dx$ બંને પદોની બાદબાકી કરતા: $\int u \frac{d^2v}{dx^2} dx - \int v \frac{d^2u}{dx^2} dx = (u \frac{dv}{dx} - \int \frac{du}{dx} \frac{dv}{dx} dx) - (v \frac{du}{dx} - \int \frac{dv}{dx} \frac{du}{dx} dx) + C$ $= u \frac{dv}{dx} - v \frac{du}{dx} - \int \frac{du}{dx} \frac{dv}{dx} dx + \int \frac{du}{dx} \frac{dv}{dx} dx + C$ $= u \frac{dv}{dx} - v \frac{du}{dx} + C$

કિંમત શોધો: $\int u \frac{d^2v}{dx^2} dx - \int v \frac{d^2u}{dx^2} dx$

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