xex as x varies from x=1 to x=3
Answers
Answer:
13.3995
Step-by-step explanation:
The average value of a continuous function
F
over an interval
[
a
,
b
]
is
1
b
−
a
∫
b
a
F
(
x
)
d
x
.
For
F
(
x
)
=
x
e
x
2
over the interval
[
0
,
2
]
, this becomes
1
2
∫
2
0
x
e
x
2
d
x
The integral can be done using the substitution
u
=
x
2
, making
d
u
=
2
x
d
x
. Also, when
x
=
0
,
u
=
0
and when
x
=
2
,
u
=
2
2
=
4
. Therefore, the quantity above can be written as
1
2
∫
4
0
1
2
e
u
d
u
=
[
1
4
e
u
]
4
0
=
1
4
e
4
−
1
4
e
0
=
1
4
e
4
−
1
4
≈
13.3995
Correct option is B)
y=x+
x
1
dx
dy
=(1−
x
2
1
)=
x
2
x
2
−1
for criticla point
x
2
x
2
−1
=0
or x=−1,+1
at x=−1, as f
′
(x) changes from +ve to −ve by going left to right, it is a point of local maxima
and f(−1)=−1+
−1
1
=−2
at x=+1, on f
′
(n) changes from −ve to +ve by going left to right, if n a point of local minima.
and f(1)=1+
1
1
=2