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Mathematics
Mathematics
Problem
Find out the area bounded by the curve
y
=
∫
1
/
8
sin
2
x
(
sin
−
1
t
)
d
t
+
∫
1
/
8
cos
2
x
(
cos
−
1
t
)
d
t
(
0
≤
x
≤
π
/
2
)
y = \int_{1/8}^{\sin^2 x} (\sin^{-1} \sqrt{t})\, dt + \int_{1/8}^{\cos^2 x} (\cos^{-1} \sqrt{t})\, dt \quad (0 \le x \le \pi/2)
y
=
∫
1/8
s
i
n
2
x
(
sin
−
1
t
)
d
t
+
∫
1/8
c
o
s
2
x
(
cos
−
1
t
)
d
t
(
0
≤
x
≤
π
/2
)
and the curve satisfying the differential equation
y
(
x
+
y
3
)
d
x
=
x
(
y
3
−
x
)
d
y
y(x + y^3)\, dx = x(y^3 - x)\, dy
y
(
x
+
y
3
)
d
x
=
x
(
y
3
−
x
)
d
y
passing through
(
4
,
−
2
)
(4, -2)
(
4
,
−
2
)
.
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