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Byju's Answer
Standard XII
Mathematics
Integration by Parts
Write the for...
Question
Write the formula for integration by parts.
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Solution
∫
f
(
x
)
.
g
(
x
)
d
x
=
f
(
x
)
∫
g
(
x
)
d
x
−
∫
f
′
(
x
)
.
(
∫
g
(
x
)
d
x
)
d
x
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0
Similar questions
Q.
Differentiate
sin
h
−
1
x
with respect to
x
.
By writing
sin
h
−
1
x
as
1
×
sin
h
−
1
x
, use integration by parts to find
∫
2
1
sin
h
−
1
d
x
Q.
Use integration by parts to evaluate
∫
2
1
cos
h
−
1
x
d
x
Q.
Assertion :
∫
d
x
x
3
√
1
+
x
4
=
−
1
2
√
1
+
1
x
4
+
C
.
Reason: For integration by parts, we have to follow ILATE rule.
Q.
Repeated application of integration by parts gives us the reduction formula, if the integrand is dependent on a natural number
n
.
If
I
n
=
∫
e
α
x
sin
n
x
d
x
=
e
α
x
α
2
+
n
sin
n
−
1
x
(
α
sin
x
−
n
cos
x
)
+
A
∫
e
α
x
sin
n
−
2
x
cos
x
, then A is equal to
Q.
Repeated application of integration by parts gives us the reduction formula, if the integrand is dependent on a natural number
n
.
If
∫
cos
m
x
sin
n
x
d
x
=
cos
m
−
1
x
(
m
−
n
)
sin
n
−
1
x
+
A
∫
cos
m
−
2
x
sin
n
x
d
x
+
C
, then
A
is equal to
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