Statement-1: ∫ − 1 3 x 2 d x does not exist Statement-2: f ( x ) = x 2 1 is discontinuous in ( − 1 , 3 ) at x = 0 and fundamental theorem of calculus applies only to continuous function.

Question

Statement-1: ∫ − 1 3 ​ x 2 d x ​ does not exist Statement-2: f ( x ) = x 2 1 ​ is discontinuous in ( − 1 , 3 ) at x = 0 and fundamental theorem of calculus applies only to continuous function.

TestHub · Accepted Answer

Statement-1 is true because the integrand f ( x ) = x 2 1 ​ has an infinite discontinuity at x = 0 within the interval [ − 1 , 3 ] . Statement-2 correctly explains this, as the Fundamental Theorem of Calculus requires the function to be continuous on the interval.

Mathematics - Definite Integration Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main (2026)