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Byju's Answer
Standard XII
Mathematics
Integration of Piecewise Continuous Functions
Evaluate: ∫...
Question
Evaluate:
∫
d
x
√
x
2
−
1
A
cos
h
(
x
)
+
c
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B
√
c
o
s
h
(
x
)
+
c
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C
√
s
i
n
h
(
x
)
+
c
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D
None of these
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Solution
The correct option is
A
cos
h
(
x
)
+
c
Given :
∫
d
x
√
x
2
−
1
∫
d
x
√
x
2
−
1
=
ln
∣
∣
x
+
√
x
2
−
1
∣
∣
=
cos
h
x
+
C
Hence the correct answer is
cos
h
x
+
C
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0
Similar questions
Q.
Show that
cos
h
x
+
sin
h
x
=
e
x
and simplify
cos
h
x
−
sin
h
x
By multiplying the expressions for
(
cos
h
x
+
sin
h
x
)
and
(
cos
h
x
−
sin
h
x
)
together, show that
cos
2
h
x
−
sin
2
h
x
=
1
Q.
Show that
cos
h
x
+
sin
h
x
=
e
x
and simplify
cos
h
x
−
sin
h
x
=
?
.
By considering
(
cos
h
x
+
sin
h
x
)
2
+
(
cos
h
x
−
sin
h
x
)
2
show that
cos
2
h
x
−
sin
2
h
x
=
cos
h
2
x
.
Q.
Use the definitions of
sin
h
x
and
cos
h
x
in terms of exponential functions to prove that
cos
h
2
x
=
1
+
2
sin
2
h
x
Q.
Assuming the derivatives of
sin
h
x
and
cos
h
x
, use the quotient rule to prove that if
y
=
tan
h
x
=
sin
h
x
cos
h
x
then
d
y
d
x
=
sec
h
2
x
.
Q.
Evaluate
∫
1
cos
h
x
+
sin
h
x
d
x
.
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