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Mathematics
Mathematics
Problem
The area enclosed by the curve
y
=
sin
x
+
cos
x
y = \sin x + \cos x
y
=
sin
x
+
cos
x
and
y
=
∣
cos
x
−
sin
x
∣
y = |\cos x - \sin x|
y
=
∣
cos
x
−
sin
x
∣
over the interval
[
0
,
π
2
]
\left[0, \frac{\pi}{2}\right]
[
0
,
2
π
]
is (A)
4
(
2
−
1
)
4(\sqrt{2}-1)
4
(
2
−
1
)
(B)
2
2
(
2
−
1
)
2\sqrt{2}(\sqrt{2}-1)
2
2
(
2
−
1
)
(C)
2
(
2
+
1
)
2(\sqrt{2}+1)
2
(
2
+
1
)
(D)
2
2
(
2
+
1
)
2\sqrt{2}(\sqrt{2}+1)
2
2
(
2
+
1
)
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