Question

What property this does this equation come under \(\int^1_{-1}\)sin⁡x dx=-\(\int_1^{-1}\)sin⁡x dx?

(a) Reverse integral property

(b) Adding intervals property

(c) Zero-length interval property

(d) Adding integrand property

I got this question during an online exam.

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

Answer 1

Right choice is (a) Reverse integral property

The best explanation: \(\int^1_{-1}\)sin⁡x dx=-\(\int_1^{-1}\)sin⁡x dx comes under the reverse integral property.

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.