Consider f: R R be a function satisfying f(2- x )=f(2+ x ) and f(20- x )=f( x ) x R . Statement-1: If ₄²⁰ f(x) d x=10 , then _ -9 ¹⁵¹ f(x) d x=90 . and Statement-2 : If f(x) is periodic with period T , then _ a ^ a + nT f( x ) dx = n ₀^ T f

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Consider f: R R be a function satisfying f(2- x )=f(2+ x ) and f(20- x )=f( x ) x R . Statement-1: If ₄²⁰ f(x) d x=10 , then _ -9 ¹⁵¹ f(x) d x=90 . and Statement-2 : If f(x) is periodic with period T , then _ a ^ a + nT f( x ) dx = n ₀^ T f( x ) dx , a R & n I .

Quantrex Academy · Accepted Answer

Correct answer: D. Statement-1 is False, Statement-2 is True.

aligned & f(2-x)=f(2+x) & x x+2 & f(-x)=f(x+4) & f(20-x)=f(x) & x x+4 & f(16-x)=f(x+4) aligned From (i) & (ii) f(-x)=f(16-x)f(x)=f(x+16) Period of f(x) is 16 . Statement-1 : ₄⁴⁺¹⁶ f(x) d x= ₀¹⁶ f( x ) dx =10 _ -9 ⁻⁹⁺¹⁶⁰ f(x) d x=10 ₀¹⁶ f(x) d x=100 Statement- 1 is false.

Consider f: R R be a function satisfying f(2- x )=f(2+ x ) and f(20- x )=f( x ) x R . Statement-1: If ₄²⁰ f(x) d x=10 , then _ -9 ¹⁵¹ f(x) d x=90 . and Statement-2 : If f(x) is periodic with period T , then _ a ^ a + nT f( x ) dx = n ₀^ T f( x ) dx , a R & n I .

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