1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider the integral I =∫1 e ( cos ( ln x )+ sin (- ln x )) dx Statement-1: I=e cos (1)-1 Statement-2: ∫ limitsab(f(x)+x f prime(x)) d x=b f(b)+a f(a)

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider the integral $I =\int_1^{ e }(\cos (\ln x )+\sin (-\ln x )) dx$
Statement-1: $I=e \cos (1)-1$
Statement-2: $\int\limits_a^b\left(f(x)+x f^{\prime}(x)\right) d x=b f(b)+a f(a)$

Integrals

Solution:

If $f ( x )=\cos (\ln x )$, then $x f ^{\prime}( x )=\sin (-\ln x )$
Statement-1 is true, statement-2 is false