समाकलन I = int_{0}^{1} x(1 - x)^n dx का मान क | vedclass

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(C) गुणधर्म $\int_{0}^{a} f(x) dx = \int_{0}^{a} f(a - x) dx$ का उपयोग करते हुए,हमें प्राप्त होता है:$I = \int_{0}^{1} (1 - x)(1 - (1 - x))^n dx$$I =

Vedclass · Accepted Answer

$\frac{1}{n + 1} - \frac{1}{n + 2}$

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(C) गुणधर्म $\int_{0}^{a} f(x) dx = \int_{0}^{a} f(a - x) dx$ का उपयोग करते हुए,हमें प्राप्त होता है:$I = \int_{0}^{1} (1 - x)(1 - (1 - x))^n dx$$I = \int_{0}^{1} (1 - x)x^n dx$$I = \int_{0}^{1} (x^n - x^{n+1}) dx$$I = \left[ \frac{x^{n+1}}{n+1} - \frac{x^{n+2}}{n+2} \right]_{0}^{1}$$I = \left( \frac{1}{n+1} - \frac{1}{n+2} \right) - (0 - 0)$$I = \frac{1}{n+1} - \frac{1}{n+2}$

समाकलन $I = \int_{0}^{1} x(1 - x)^n dx$ का मान क्या है?

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