`int_(0)^(pi//4)sec^(7)theta*sin^(3)d theta` का मान है

Options

A. `(3)/(12)`
B. `(5)/(12)`
C. `(3)/(4)`
D. इनमें से कोई नहीं

Answer

B

Explanation

`I=int_(0)^(pi//4)sec^(7)thetasin^(3)thetad theta`
`=int_(0)^(pi//4)sec^(4)thetatan^(3)theta d theta`
`=int_(0)^(pi//4)(1+tan^(2)theta)tan^(3)thetasec^(2)thetad theta` माना `tan theta =trArrsec^(2)thetad theta=dt`
`thereforeI=int_(0)^(1)(1+t^(2))t^(3)dt=[(t^(4))/(4)+(t^(6))/(6)]_(0)^(1)`
`=(1)/(4)=(1)/(6)=(5)/(12)`