Multiplex for JEE 2 (no way out)

Calculus Level 4

∫ 0 1 ( ∏ r = 1 n ( x + r ) ) ( ∑ k = 1 n 1 x + k ) d x = ? \displaystyle \int_{0}^{1} \left (\prod_{r=1}^{n}(x+r) \right ) \left (\sum_{k=1}^{n}\frac{1}{x+k} \right ) \ dx = \ ?

This is a problem of my set Some JEE problems .
0 0 n ( n ! ) n(n!) n ( n + 1 ) ! n(n+1)! 1 1 ( n + 1 ) ! (n+1)! n ! n! e n ! e^{n!} The integral is not solvable

View wiki
Tanishq Varshney by Tanishq Varshney , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Incredible Mind
Feb 18, 2015

just sub the first infinite product as u..the 2nd fcn will give du/u

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Akhilesh Vibhute
Nov 30, 2015

Verify for n = 2, 3 ... Simple Life becomes absolutely easier :-)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...