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Mathematics
Problem
The value of
t
t
t
for which
∫
0
π
2
(
sin
x
+
t
cos
x
)
d
x
∫
0
π
2
(
sin
x
+
t
cos
x
)
2
d
x
\frac{\int_0^{\frac{\pi}{2}} (\sin x + t \cos x) \, dx}{\sqrt{\int_0^{\frac{\pi}{2}} (\sin x + t \cos x)^2 \, dx}}
∫
0
2
π
(
sin
x
+
t
cos
x
)
2
d
x
∫
0
2
π
(
sin
x
+
t
cos
x
)
d
x
is maximum lies in the interval (a)
(
0
,
1
2
)
(0, \frac{1}{2})
(
0
,
2
1
)
(b)
(
1
2
,
3
4
)
(\frac{1}{2}, \frac{3}{4})
(
2
1
,
4
3
)
(c)
(
3
4
,
3
2
)
(\frac{3}{4}, \frac{3}{2})
(
4
3
,
2
3
)
(d)
(
3
2
,
5
2
)
(\frac{3}{2}, \frac{5}{2})
(
2
3
,
2
5
)
(a)
(
0
,
1
2
)
(0, \frac{1}{2})
(
0
,
2
1
)
(b)
(
1
2
,
3
4
)
(\frac{1}{2}, \frac{3}{4})
(
2
1
,
4
3
)
(c)
(
3
4
,
3
2
)
(\frac{3}{4}, \frac{3}{2})
(
4
3
,
2
3
)
(d)
(
3
2
,
5
2
)
(\frac{3}{2}, \frac{5}{2})
(
2
3
,
2
5
)
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