A calculus problem by Sharad Roy

Calculus Level 2

F i n d t h e v a l u e o f ∫ 0 10 6 + 6 + 6 + 6 + . . . . . . . ∞ d x Find\quad the\quad value\quad of\quad \\ \\ \int _{ 0 }^{ 10 }{ \sqrt { 6+\sqrt { 6+\sqrt { 6+\sqrt { 6+.......\infty } } } } } dx


The answer is 30.

Sharad Roy by Sharad Roy , 22, 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.

1 solution

L N
Jun 6, 2014

Let S = 6 + 6... S = \sqrt{6 + \sqrt{6 ... } } Then, S = 6 + S S = \sqrt{6+S} . Simplify: S 2 = S + 6 S^2 = S + 6 , S 2 − S − 6 = 0 S^2 - S - 6 = 0 , ( S + 2 ) ( S − 3 ) = 0 (S+2)(S-3) = 0 , Clearly S S cannot be negative, therefore, S = 3 S = 3 , Now, ∫ 0 10 3 = 3 ( 10 ) − 0 = 30 \int_{0}^{10} 3 = 3(10)-0 = 30

6 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...