integrate f(x) dx limit 1 to 4
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Answer:
Step-by-step explanation:
∫
4
1
(
√
x
)
d
x
note
√
x
=
x
1
2
=
∫
4
1
(
x
1
2
)
d
x
integrate using the
power rule
∙
x
∫
(
a
x
n
)
d
x
=
a
n
+
1
x
n
+
1
;
n
≠
−
1
⇒
F
(
x
)
=
[
1
3
2
x
3
2
]
4
1
⇒
F
(
x
)
=
[
2
3
x
3
2
]
4
1
[
F
(
x
)
=
F
(
b
)
−
F
(
a
)
→
a
=
1
,
b
=
4
]
⇒
F
(
x
)
=
(
2
3
)
.4
3
2
−
(
2
3
)
.1
⇒
F
(
x
)
=
16
3
−
2
3
=
14
3
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