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If , and then the value of…
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
If
f
′
(
x
)
=
tan
−
1
(
sec
x
+
tan
x
)
f'(x) = \tan^{-1}(\sec x + \tan x)
f
′
(
x
)
=
tan
−
1
(
sec
x
+
tan
x
)
,
x
∈
(
−
π
2
,
π
2
)
x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
x
∈
(
−
2
π
,
2
π
)
and
f
(
0
)
=
0
f(0) = 0
f
(
0
)
=
0
then the value of
f
(
1
)
f(1)
f
(
1
)
is (a)
π
+
1
4
\frac{\pi+1}{4}
4
π
+
1
(b)
π
−
1
4
\frac{\pi-1}{4}
4
π
−
1
(c)
π
+
1
2
\frac{\pi+1}{2}
2
π
+
1
(d) 0
Related theory
Inverse Trigonometric Functions
Trigonometric Functions
Antiderivatives
Standard algebraic integrals
Integrals of standard functions
Integrals
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