Question

What is the name of the property of \(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x)  dx?

(a) Zero interval property

(b) Adding intervals property

(c) Adding integral property

(d) Adding integrand property

The question was asked during an internship interview.

Query is from Properties of Definite Integrals in chapter Integrals of Mathematics – Class 12

Answer 1

Correct answer is (b) Adding intervals property

The explanation is: \(\int_a^b\)f(x)dx+\(\int_b^c\)(x)dx = \(\int_a^c\)f(x) dx is a property of definite integrals. \(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx is called as adding intervals property used to combine a lower limit and upper limit of two different integrals.