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Mathematics
Problem
The area of the region above the x-axis bounded by the curve
y
=
tan
x
y = \tan x
y
=
tan
x
,
0
≤
x
≤
π
2
0 \le x \le \frac{\pi}{2}
0
≤
x
≤
2
π
and the tangent to the curve at
x
=
π
4
x = \frac{\pi}{4}
x
=
4
π
is : [JEE-MAIN ONLINE-2014] (1)
1
2
(
1
+
log
2
)
\frac{1}{2}(1 + \log 2)
2
1
(
1
+
lo
g
2
)
(2)
1
2
(
log
2
+
1
2
)
\frac{1}{2}\left(\log 2 + \frac{1}{2}\right)
2
1
(
lo
g
2
+
2
1
)
(3)
1
2
(
1
−
log
2
)
\frac{1}{2}(1 - \log 2)
2
1
(
1
−
lo
g
2
)
(4)
1
2
(
log
2
−
1
2
)
\frac{1}{2}\left(\log 2 - \frac{1}{2}\right)
2
1
(
lo
g
2
−
2
1
)
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