Let the domain of the function f(x) = log ₄(log ₅(log ₃(18x - x² - 77))) be (a, b). Then the value of the integral ∫ a ^(b) (sin ³x)/((sin ³x + sin ³(a + b - x)) dx is equal to _ _ _ _ _ _ _.

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Jul, Morning shift · Q35

JEE Main 202127 Jul, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Let the domain of the function

f(x) = {\log _4}\left( {{{\log }_5}\left( {{{\log }_3}(18x - {x^2} - 77)} \right)} \right)

be (a, b). Then the value of the integral

\int\limits_a^b {{{{{\sin }^3}x} \over {({{\sin }^3}x + {{\sin }^3}(a + b - x)}}} dx

is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Integral Calculus Question with Answer (27 Jul Morning shift, Q35) | JEE Arc

JEE Main 2021 · 27 Jul, Morning shift · Q35

JEE Main 202127 Jul, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Let the domain of the function

f(x) = {\log _4}\left( {{{\log }_5}\left( {{{\log }_3}(18x - {x^2} - 77)} \right)} \right)

be (a, b). Then the value of the integral

\int\limits_a^b {{{{{\sin }^3}x} \over {({{\sin }^3}x + {{\sin }^3}(a + b - x)}}} dx

is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.