For m, n > 0, let α(m, n)=∫₀² t^(m)(1+3 t)ⁿ d t. If 11 α(10,6)+18 α(11,5)=p(14)⁶, then p is equal to _ _ _ _ _ _.

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Morning shift · Q31

JEE Main 202311 Apr, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

For

m, n > 0

, let

\alpha(m, n)=\int_\limits{0}^{2} t^{m}(1+3 t)^{n} d t

. If

11 \alpha(10,6)+18 \alpha(11,5)=p(14)^{6}

, then

p

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.