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Let F(x) be an indefinite integral of si...

Let F(x) be an indefinite integral of `sin^(2)x`
Statement-1: The function F(x) satisfies `F(x+pi)=F(x)` for all real x. because
Statement-2: `sin^(3)(x+pi)=sin^(2)x` for all real x.
A) Statement-1: True , statement-2 is true, Statement -2 is not a correct explanation for statement -1
c) Statement-1 is True, Statement -2 is False.
D) Statement-1 is False, Statement-2 is True.

A

Both the Statement are true and Statement 2 is the correct explanation of Statement 1

B

Both the Statement are true but Statement 2 is not the correct explanation of Statement 1

C

Statement 1 is true but Statement 2 is false

D

Statement 1 is false but Statement 2 is true

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x) = int sin^(2) x.dx = int (1 - cos 2x)/(2) .dx`
`= (1)/(2) x - (sin 2x)/(2) (1)/(2) + c = (1)/(2)x - (1)/(4) sin 2x + c`
(i) `f(pi + x) = (1)/(2) (pi + x) - (1)/(4) sin 2 (pi + x)`
`= (1)/(2) pi + (1)/(2) x - (1)/(2) sin (2pi + 2x) + c`
`= (x)/(2) - (1)/(2) sin 2x + c = f (x)`
So, statement 1 is true
(ii) `sin^(2) (pi + x) = sin^(2)x`
`(-sin x)^(2) = sin^(2)x`
`rArr sin^(2) x = sin^(2) x`
So, statement 2 is true
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