Question

Identify the zero-length interval property.

(a) \(\int_a^b\)f(x)dx = -1

(b) \(\int_a^b\)f(x)dx = 1

(c) \(\int_a^b\)f(x)dx = 0

(d) \(\int_a^b\)f(x)dx = 0.1

I have been asked this question in an internship interview.

This intriguing question comes from Properties of Definite Integrals topic in chapter Integrals of Mathematics – Class 12

Answer 1

Right answer is (c) \(\int_a^b\)f(x)dx = 0

Best explanation: The zero-length interval property is one of the properties used in definite integrals and they are always positive. The zero-length interval property is \(\int_a^b\)f(x)dx = 0.