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प्रश्न
If `I_n = int_0^(pi/4) tan^n theta "d"theta " then " I_8 + I_6` equals ______.
पर्याय
`1/4`
`1/5`
`1/6`
`1/7`
MCQ
रिकाम्या जागा भरा
उत्तर
If `I_n = int_0^(pi/4) tan^n theta "d"theta " then " I_8 + I_6` equals `1/7`.
Explanation:
`I_8 + I_6 = int_0^(pi/4) (tan^8theta + tan^6theta) "d"theta`
= `int_0^(pi/4) tan^6theta sec^2theta "d"theta`
Put tan θ = t ⇒ sec2θ dθ = dt
`therefore I_8 + I_6 = int_0^1 "t"^6 "dt" = ["t"^7/7]_0^1 = 1/7`
shaalaa.com
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