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Let F(x)=int(a)^(x^(2)) cos sqrt(t)dt ...

Let F(x)`=int_(a)^(x^(2)) cos sqrt(t)dt`
Statement-1: F'(x)=cos x
Statement-2: If f(x)`=int_(a)^(x) phi(t) dt`, then f'(x)=`phi`(x).

A

Statement-1 is true, Statement-2 is True,Statement-2 is a correct explanation for Statement-1.

B

Statement-1 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.

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`F(x)=underset(1)overset(x^(2))int cos sqrt(t)dt`
`rArr F'(x)=underset(1)overset(x^(2))int 0 dt+(d)/(dx)(x^(2))cos x-(d)/(dx)(1)cos 1=2x cos x`
So, statement-1 is not true. Clearly, statement-2 is true.
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