📐 Mathematics · Integrals · JEE

The value of the definite integral of the greatest integer function [x] from 0 to 2 is:

Answer: 1.

Correct answer: B. 1

Explanation: [x] = 0 on [0,1) and 1 on [1,2), so the integral is 0·1 + 1·1 = 1.

The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.

Concept context

Indefinite and definite integrals, areas under curves