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The value of int(0)^(pi//4) (tan^(n)x+...

The value of
`int_(0)^(pi//4) (tan^(n)x+tan^(n-2)x)d(x-([x])/(1!)+([x]^(2))/(2!)-([x]^(3))/(3!)+....)`
where [x] is greatest function, is

A

`(1)/(n)`

B

`(1)/(n+2)`

C

`(1)/(n-1)`

D

`(1)/(n-2)`

Text Solution

Verified by Experts

The correct Answer is:
C
For `x in[0,pi//4],[x]=0`
`:.underset(0)overset(pi//4)int (tan^(n)x+tan^(n-2)x)d(x-([x])/(1!)+([x]^(2))/(2!)-([x]^(3))/(3!)+....)`
`=underset(0)overset(pi//4)int tan^(n-2)x sec^(2)x dx=[(tan^(n-1)x)/(n-1)]_(0)^(pi//4)=(1)/(n-1)`
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Section I - Solved Mcqs
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