Let $\beta(m, n)=\int_\limits0^1 x^{m-1}(1-x)^{n-1} d x, m, n>0.$ If $\int_\limits 0^1\left(1-{x}^{10}\right)^{20} {dx}={a} \times \beta({b}, {c}),$ then $100({a}+{b}+{c})$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

\beta(m, n)=\int\limits_{0}^1 x^{m-1}(1-x)^{n-1} d x, m, n>0.

\int\limits_{0}^1\left(1-{x}^{10}\right)^{20} {dx}={a} \times \beta({b}, {c}),

then

100({a}+{b}+{c})

equals

View answer and explanation

Correct option: D

2120

Option D (2120) is correct because the integral is evaluated using substitution and the properties of the Beta function.

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