Problem 57993. Easy Sequences 110: Integration of the Sum of a Recursive Trigonometric Function
A trigonometric function,
, is defined as follows:
Applying
recursively we define another function
, for integer n:
We then define
as the sum of value of R from 1 to n:
Finally, we are asked to evaluate the integral of S with respect to x, over the real range
:
For example for
,
,
, we have:
>> a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)
a = 7.05797686912156
Please present the final output rounded-off to 6 decimal places. Therefore the final answer is
.
-------------------------
NOTE: There are a number of ways to do numerical Integration in Matlab. Just make sure that the output would be accurate within 6 decimal places of the value obtained using the integral function shown above.
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