Let = _ 0 ^ 1 d x 1+x^ 3 , p= _ n [ _ r=1 ^ n (n^ 3 +r^ 3 ) n^ 3 n ]^ 1 / n then ln p is…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Let \[\lambda=\int_{0}^{1} \frac{d x}{1+x^{3}}, p=\lim _{n \rightarrow \infty}\left[\frac{\prod_{r=1}^{n}\left(n^{3}+r^{3}\right)}{n^{3 n}}\right]^{1 / n}\] then ln p is equal to
- \(\ln 2-1+\lambda\)
- \(\ln 2-3+3 \lambda\)
- \(2 \ln 2-\lambda\)
- \(\ln 4-3+3 \lambda\)
Answer
(B) 2-3+3
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The value of _ ^ 2 [2 x] d x where [⋅] represents the greatest integer function is
- If F(x)= 1 x^ 2 _ 4 ^ x (4 t^ 2 -2 F^ (t) ) d t then F^ (4) equals –
- Let a , b , c be non zero real numbers such that _ 0 ^ 1 (1+ ^ 8 x ) (a x^ 2 +b x+c ) d x= _ 0 ^ 2 (1+ ^ 8 x…
- If I = ^ 7 x ~d x then I equals
- Let g(x)= _ 0 ^ x f(t) d t , where f is such that 1 2 f(t) 1 for t [0,1] and 0 f(t) 1 2 for t [1,2] then g…
- The value of the function f(x)=1+x+ _ 1 ^ x ( ^ 2 t+2 t ) d t where f^ (x) vanishes is
- Consider the integrals I_ 1 = _ 0 ^ 1 e^ -x ^ 2 x d x, I_ 2 = _ 0 ^ 1 e^ -x^ 2 ^ 2 x d x I_ 3 = _ 0 ^ 1 e^ …
- The area bounded by the curves y = f ( x ), the x -axis and the ordinates x = 1, x = b is ( b – 1) sin (3 b +…
More Integral Calculus questions · Browse all practice questions