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Standard XII
Mathematics
Integration by Substitution
Question
Prove that
∫
d
x
√
[
(
x
−
a
)
]
(
x
−
b
)
equal to
log
(
−
2
(
√
(
a
−
x
)
(
b
−
x
)
+
x
)
+
a
+
b
)
+
c
.
Open in App
Solution
Verified by Toppr
I
=
∫
1
√
(
x
−
a
)
(
x
−
b
)
d
x
.
Put
x
=
u
2
−
a
b
−
a
−
b
+
2
u
⇒
d
x
=
(
2
u
−
a
−
b
+
2
u
−
2
(
u
2
−
a
b
)
(
−
a
−
b
+
2
u
)
2
)
d
u
∴
I
=
−
∫
2
a
+
b
−
2
u
d
u
.
s
=
a
+
b
−
2
u
⇒
d
s
−
2
d
u
∴
I
=
∫
1
s
d
S
=
log
s
+
c
=
log
(
a
+
b
−
2
u
)
+
c
=
log
(
−
2
(
√
(
a
−
x
)
(
b
−
x
)
+
x
)
+
a
+
b
)
+
c
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Similar Questions
Q1
Prove that
∫
d
x
√
[
(
x
−
a
)
]
(
x
−
b
)
equal to
log
(
−
2
(
√
(
a
−
x
)
(
b
−
x
)
+
x
)
+
a
+
b
)
+
c
.
View Solution
Q2
If
y
=
a
cos
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)
+
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(
log
x
)
then prove that
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2
d
2
y
d
x
2
+
x
d
y
d
x
+
y
=
0
.
View Solution
Q3
∫
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b
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+
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(
c
)
cos
e
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x
-
b
)
sin
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Q4
Prove that
y
=
a
c
o
s
(
l
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g
x
)
+
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i
n
(
l
o
g
x
)
is the solution of
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2
d
2
y
d
x
2
+
x
d
y
d
x
+
y
=
0.
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Q5
If
2
log
b
x
=
1
log
a
x
+
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log
c
x
then prove that
a
,
b
,
c
are in
G
P
.
Where
(
a
,
b
,
c
&
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)
&
≠
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)
View Solution