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Let on . How many distinct values of in satisfy…
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
Let
f
(
x
)
=
sin
x
+
x
2
f(x)=\sin x + x^{2}
f
(
x
)
=
sin
x
+
x
2
on
[
0
,
π
]
[0,\pi]
[
0
,
π
]
. How many distinct values of
c
c
c
in
(
0
,
π
)
(0,\pi)
(
0
,
π
)
satisfy
∫
0
π
f
(
x
)
d
x
=
f
(
c
)
π
\displaystyle \int_{0}^{\pi} f(x)\,dx = f(c)\,\pi
∫
0
π
f
(
x
)
d
x
=
f
(
c
)
π
? (a) Exactly two (b) None (c) Exactly one (d) More than two
Related theory
Continuity
Applications of Integration
Fundamental theorem of calculus
Definite integrals
Integrals
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