Question

What is adding intervals property?

(a) \(\int_a^c\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx

(b) \(\int_a^b\)f(x)dx+\(\int_b^a\)f(x)dx = \(\int_a^c\)f(x) dx

(c) \(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx

(d) \(\int_a^b\)f(x)dx-\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx

This question was posed to me in an interview for job.

I'm obligated to ask this question of Properties of Definite Integrals in section Integrals of Mathematics – Class 12

Answer 1

The correct choice is (c) \(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx

To explain I would say: The adding intervals property of definite integrals is \(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx.

\(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx