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For any real constant and differentiable function
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
For any real constant
k
k
k
and differentiable function
f
f
f
, which of the following identities is always true? (a)
∫
k
f
(
x
)
d
x
=
k
f
(
x
)
+
C
\displaystyle \int k\,f(x)\,dx = k\,f(x) + C
∫
k
f
(
x
)
d
x
=
k
f
(
x
)
+
C
(b)
∫
k
f
(
x
)
d
x
=
1
k
∫
f
(
x
)
d
x
+
C
\displaystyle \int k\,f(x)\,dx = \dfrac{1}{k}\int f(x)\,dx + C
∫
k
f
(
x
)
d
x
=
k
1
∫
f
(
x
)
d
x
+
C
(c)
∫
k
f
(
x
)
d
x
=
k
∫
f
(
x
)
d
x
+
C
\displaystyle \int k\,f(x)\,dx = k\int f(x)\,dx + C
∫
k
f
(
x
)
d
x
=
k
∫
f
(
x
)
d
x
+
C
(d)
∫
k
f
(
x
)
d
x
=
∫
f
(
k
x
)
d
x
+
C
\displaystyle \int k\,f(x)\,dx = \int f(kx)\,dx + C
∫
k
f
(
x
)
d
x
=
∫
f
(
k
x
)
d
x
+
C
Related theory
Antiderivatives
Standard algebraic integrals
Integration as inverse process of differentiation
Integrals
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