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Mathematics
Mathematics
Problem
A point
(
x
,
y
)
(x,y)
(
x
,
y
)
in the first quadrant satisfies
x
2
+
y
2
=
25
x^{2}+y^{2}=25
x
2
+
y
2
=
25
. Define
F
(
x
)
=
∫
0
y
(
3
t
−
t
2
)
d
t
.
F(x)=\int_{0}^{y} \bigl(3t-t^{2}\bigr)\,dt.
F
(
x
)
=
∫
0
y
(
3
t
−
t
2
)
d
t
.
Find
d
F
d
x
\dfrac{dF}{dx}
d
x
d
F
at
x
=
3
x=3
x
=
3
.
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