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UPSEE 2019 Solved Paper
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© examsnet.com
Question : 122
Total: 150
If
J
=
π
∕
3
∫
π
∕
6
1
√
cos
x
+
√
sin
x
d
x
, then
π
∕
3
∫
π
∕
6
x
√
cos
x
+
√
sin
x
d
x
equals
π
6
J
π
3
J
π
4
J
π
J
Validate
Solution:
We have,
J
=
π
∕
3
∫
π
∕
6
1
√
cos
x
+
√
sin
x
d
x
Let
I
=
π
∕
3
∫
π
∕
6
x
√
cos
x
+
√
sin
x
d
x
On applying
b
∫
a
f
(
x
)
=
b
∫
a
f
(
a
+
b
−
x
)
d
x
I
=
π
∕
3
∫
π
∕
6
π
3
+
π
6
−
x
√
cos
(
π
3
+
π
6
−
x
)
+
√
sin
(
π
3
+
π
6
−
x
)
d
x
I
=
π
∕
3
∫
π
∕
6
π
∕
2
−
x
√
sin
x
+
√
cos
x
d
x
2
I
=
π
∕
3
∫
π
∕
6
π
∕
2
√
sin
x
+
√
cos
x
d
x
2
I
=
π
2
J
I
=
π
4
J
© examsnet.com
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