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The value of (where
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
The value of
∫
0
π
/
4
(
tan
n
(
x
−
[
x
]
)
+
tan
n
−
2
(
x
−
[
x
]
)
)
d
x
\int_{0}^{\pi/4} (\tan^n(x - [x]) + \tan^{n-2}(x - [x])) dx
∫
0
π
/4
(
tan
n
(
x
−
[
x
])
+
tan
n
−
2
(
x
−
[
x
]))
d
x
(where,
[
⋅
]
[\cdot]
[
⋅
]
denotes greatest integer function) is equal to (1)
1
n
\frac{1}{n}
n
1
(2)
1
n
−
1
\frac{1}{n-1}
n
−
1
1
(3)
1
n
(
n
−
1
)
\frac{1}{n(n-1)}
n
(
n
−
1
)
1
(4)
1
n
(
n
+
1
)
\frac{1}{n(n+1)}
n
(
n
+
1
)
1
Related theory
Antiderivatives
Integration Techniques
Standard trigonometric integrals
Integration using trigonometric identities
Integrals
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