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Class 12 Engineering Maths
Integrals
Integrals - Class 12 Engineering Maths - Extra Questions
The value of the definite integral,
I
=
∫
√
10
0
x
e
x
2
d
x
is equal to
∫
2
π
0
cos
5
x
d
x
Write the value of
∫
1
−
sin
x
cos
2
x
d
x
√
2
∫
2
π
0
√
1
−
sin
x
d
x
=
Prove that:
∫
π
0
x
d
x
1
+
sin
x
=
π
Evaluate the following definite integral:
∫
12
4
x
d
x
Evaluate the following definite integral:
∫
π
/
2
0
sin
x
cos
x
d
x
Evaluate the f
ollowing definate integral:
∫
2
0
3
x
+
2
d
x
∫
1
0
d
x
(
1
+
x
)
√
(
2
+
x
−
x
2
)
=
1
k
√
2
. Find the value of
k
.
Integrate
∫
1
0
sin
−
1
(
2
x
1
+
x
2
)
d
x
Evaluate:
∫
1
0
x
4
(
1
−
x
)
4
1
+
x
2
d
x
∫
1
0
cot
−
1
(
1
+
x
2
−
x
)
d
x
.
Prove that
∫
tan
x
1
/
e
t
1
+
t
2
d
t
+
∫
cot
x
1
/
e
1
t
(
1
+
t
2
)
d
t
=
1
.
Evaluate:
∫
π
/
4
0
sin
x
+
cos
x
9
+
16
sin
2
x
d
x
Evaluate:
0
∫
2
1
√
4
−
x
2
d
x
EVALUATE
∫
3
2
1
x
+
5
d
x
Evaluate the definite integral:
∫
1
0
1
−
x
2
(
1
+
x
2
)
2
d
x
Evaluate:
∫
1
2
x
+
3
d
x
Evaluate the following integrals:
∫
√
2
x
2
+
3
x
+
4
d
x
Evaluate the following integral:
∫
(
x
+
1
)
√
2
x
2
+
3
d
x
Evaluate the following integrals:
∫
√
2
a
x
−
x
2
d
x
Evaluate the following definite integral:
∫
π
/
4
0
sin
3
2
t
cos
2
t
d
t
.
Evaluate the following integral:
∫
2
0
x
√
2
−
x
d
x
.
Evaluate the following integral:
∫
9
0
d
x
(
1
+
√
x
)
.
Evaluate the following integral:
∫
3
2
(
2
−
x
)
√
5
x
−
6
−
x
2
d
x
.
Evaluate the following integral:
∫
a
0
x
√
a
2
+
x
2
d
x
.
Evaluate the following integral:
∫
2
1
d
x
(
x
+
1
)
√
x
2
−
1
.
Evaluate the following integral:
∫
1
0
x
3
√
1
+
3
x
4
d
x
.
Evaluate the following integral:
∫
a
0
x
4
√
a
2
−
x
2
d
x
.
Evaluate the following integral:
∫
1
0
(
1
−
x
2
)
(
1
+
x
2
)
2
d
x
.
Prove that
∫
4
1
√
x
(
√
5
−
x
+
√
x
)
d
x
=
3
2
.
Prove that
∫
1
0
x
(
1
−
x
)
5
d
x
=
1
42
.
Prove that
∫
∞
0
x
(
1
+
x
)
(
1
+
x
2
)
d
x
=
π
4
.
Prove that
∫
3
a
/
4
a
/
4
√
x
(
√
a
−
x
+
√
x
)
d
x
=
a
4
.
Prove that
∫
8
0
|
x
−
5
|
d
x
=
17
.
Prove that
∫
a
0
√
x
(
√
x
+
√
a
−
x
)
d
x
=
a
2
.
Prove that
∫
a
0
d
x
x
+
√
a
2
−
x
2
=
π
4
.
Prove that
∫
2
0
x
√
2
−
x
d
x
=
16
√
2
15
.
Prove that
∫
2
−
2
|
x
+
1
|
d
x
=
5
.
The value of the integral
9999
∫
∞
0
d
x
(
x
+
√
1
+
x
2
)
100
is
Let
I
=
∫
1
0
d
x
√
4
−
x
2
−
x
3
and
I
1
=
∫
1
/
2
0
d
x
√
1
−
x
4
Find :
∫
π
2
0
d
x
4
+
5
cos
x
d
x
∫
π
/
4
0
(
s
i
n
x
+
c
o
s
x
)
9
+
16
s
i
n
2
x
d
x
∫
2
1
x
√
2
x
2
+
1
d
x
Evaluate:
∫
√
3
1
d
x
1
+
x
2
Evaluate:
∫
π
2
0
sin
x
⋅
cos
x
1
+
sin
4
x
⋅
d
x
.
If the value of the definite integral
∫
207
0
C
7
x
200
⋅
(
1
−
x
)
7
d
x
is equal to
1
k
where
k
∈
N
, then
the value of
k
/
26
is
Class 12 Engineering Maths Extra Questions
Continuity And Differentiability Extra Questions
Determinants Extra Questions
Differential Equations Extra Questions
Integrals Extra Questions
Inverse Trigonometric Functions Extra Questions
Relations And Functions Extra Questions
Three Dimensional Geometry Extra Questions
Vector Algebra Extra Questions
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