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Standard X
Mathematics
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ntIf f(x) be ...
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ntIf f(x) be a periodic function of period t show that, [ integral f(x) dx, with lower limit 'a' and upper limit 'a+t'] is independent of a.n
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Similar questions
Q.
If
f
(
x
)
is a continuous periodic function with period T, then the integral
I
=
∫
a
+
t
a
f
(
x
)
d
x
is
Q.
Assertion :Consider the function
f
(
x
)
satisfying the relation
f
(
x
+
1
)
+
f
(
x
+
7
)
=
0
∀
x
∈
R
.
The possible least value of
t
for which
∫
a
+
t
a
f
(
x
)
d
x
is independent of
a
is
12
Reason:
f
(
x
)
is a periodic function.
Q.
Assertion :A function
f
satisfies the condition
f
(
x
+
T
)
=
1
+
{
1
−
3
f
(
x
)
+
3
(
f
(
x
)
)
2
−
(
f
(
x
)
)
3
}
1
/
3
(where
T
is a fixed positive number) is periodic with period
2
T
. Reason: If
f
(
x
+
2
T
)
=
f
(
x
)
then period of
f
(
x
)
is
2
T
.
Q.
Assertion :Let F(x) be an indefinite integral of
s
i
n
8
x
.
Statement 1:
F
(
x
)
−
35
128
x
is a periodic function with period
π
. Reason: Statement 2: The period of
s
i
n
n
α
x
is
2
π
/
a
.
Q.
lf
f
(
x
)
is a periodic function with period T, then
∫
b
+
2
T
a
+
2
T
f
(
x
)
d
x
is equal to
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