integration of square root of 14x-20-2x^2.dx
Answers
Answered by
2
Answer:
How do you find the integral of
∫
√
14
x
−
x
2
d
x
?
Calculus Integrals of Trigonometric Functions
2 Answers
Sasha P.
Sep 27, 2015
49
2
arcsin
(
x
−
7
7
)
+
49
4
sin
2
arcsin
(
x
−
7
7
)
+
C
Explanation:
∫
√
14
x
−
x
2
d
x
=
∫
√
49
−
49
+
14
x
−
x
2
d
x
=
=
∫
√
49
−
(
x
−
7
)
2
d
x
=
7
∫
√
1
−
(
x
−
7
7
)
2
d
x
=
I
x
−
7
7
=
sin
t
⇒
d
x
=
7
cos
t
d
t
I
=
49
∫
√
1
−
sin
2
t
cos
t
d
t
=
49
∫
√
cos
2
t
cos
t
d
t
=
I
=
49
∫
cos
2
t
d
t
=
49
∫
1
+
cos
2
t
2
d
t
=
49
2
(
t
+
1
2
sin
2
t
)
+
C
I
=
49
2
arcsin
(
x
−
7
7
)
+
49
4
sin
2
arcsin
(
x
−
7
7
)
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