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Integral calculus
Properties of the integral
MCQ
For f and g continuous on [a;b] and a < c < b, which of the following statements are true?
Possible answers
∫
a
b
f
=
∫
a
c
f
+
∫
c
b
f
\displaystyle\int_a^b f = \int_a^c f + \int_c^b f
∫
a
b
f
=
∫
a
c
f
+
∫
c
b
f
∫
a
b
f
=
(
∫
a
c
f
)
(
∫
c
b
f
)
\displaystyle\int_a^b f = \left(\int_a^c f\right)\left(\int_c^b f\right)
∫
a
b
f
=
(
∫
a
c
f
)
(
∫
c
b
f
)
∫
a
b
(
f
+
g
)
=
∫
a
b
f
+
∫
a
b
g
\displaystyle\int_a^b (f + g) = \int_a^b f + \int_a^b g
∫
a
b
(
f
+
g
)
=
∫
a
b
f
+
∫
a
b
g
∫
b
a
f
=
∫
a
b
f
\displaystyle\int_b^a f = \int_a^b f
∫
b
a
f
=
∫
a
b
f
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