Question

Let the domain of the function 

f(x) = log₄ (log₅ (log₃(18x - x² - 77))) be (a, b) then the value of the integral

\(\int \limits_a^b \frac{sin^3x}{(sin^3 x + sin^3(a + b -x))}\) dx is equal to .............. 

∫sin³x/(sin³x + sin³(a + b - x)) x ∈ [b, a]

Answer 1

For domain 

log₅(log₃(18x - x² - 77)) > 0

log₃ (18x - x² - 77) > 1

18x - x² - 77 > 3

 x² - 18x + 80 <0

x ∈ (8, 10)

\(\Rightarrow\) a = 8 and b = 0