
Define a function
Where n is a fixed natural number. Then is.
Answer
531k+ views
Hint:- Check values of in different ranges from .
As we know that we had to find the value of .
Where, (1)
So, from equation 1, we can see that the value of will be,
for x in range (2)
for x in range (3)
So, to find the value of we had to break the limits of the integral into two parts,
So, (4)
And, from equation 2
As, we know that for x in range .
So,
Now we had to solve the above equation.
So, solving the above equation. It becomes,
(5)
And, from equation 3
So, for x in range
So, solving the above equation. It becomes,
(6)
Now, putting the value of and from equation 5 and 6 to equation 4.
So,
Hence, the correct option will be D.
Note:- Whenever we came up with this type of problem then we should break the
limits of integral according to the value of function in different ranges. Otherwise
solving the given integral without checking the value of integral in different integral
will give us incorrect answers.
As we know that we had to find the value of
So, from equation 1, we can see that the value of
So, to find the value of
As, we know that
Now we had to solve the above equation.
So, solving the above equation. It becomes,
So, solving the above equation. It becomes,
Now, putting the value of
Hence, the correct option will be D.
Note:- Whenever we came up with this type of problem then we should break the
limits of integral according to the value of function in different ranges. Otherwise
solving the given integral without checking the value of integral in different integral
will give us incorrect answers.
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