Question

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

(a) Reverse integral property

(b) Adding intervals property

(c) Zero interval property

(d) Adding integrand property

I had been asked this question in an interview for job.

Question is from Properties of Definite Integrals topic in division Integrals of Mathematics – Class 12

Answer 1

The correct option is (a) Reverse integral property

To explain I would say: In the reverse integral property the upper limits and lower limits are interchanged. The reverse integral property of definite integrals is \(\int_a^b\)f(x)dx=-\(\int_b^a\)f(x)dx.