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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
,
g
(
x
)
=
cos
x
g(x) = \cos x
g
(
x
)
=
cos
x
and
α
,
β
(
α
<
β
)
\alpha, \beta (\alpha < \beta)
α
,
β
(
α
<
β
)
be the roots of the equation
18
x
2
−
9
π
x
+
π
2
=
0
18x^2 - 9\pi x + \pi^2 = 0
18
x
2
−
9
π
x
+
π
2
=
0
. Then, the area bounded by the curves
y
=
f
∘
g
(
x
)
y = f \circ g(x)
y
=
f
∘
g
(
x
)
, the ordinates
x
=
α
,
x
=
β
x = \alpha, x = \beta
x
=
α
,
x
=
β
and the
X
X
X
-axis is a.
1
2
(
π
−
3
)
\frac{1}{2}(\pi - 3)
2
1
(
π
−
3
)
sq units b.
π
3
\frac{\pi}{3}
3
π
sq units c.
π
4
\frac{\pi}{4}
4
π
sq units d.
π
12
\frac{\pi}{12}
12
π
sq units
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