If f ( x ) = ∫ 1/ x x cos t 2 d t ( x > 0 ) then d x df ( x ) is

d x df ( x ) = cos ( x ) 2 d x d x − cos ( x 1 ) 2 ⋅ d x d ( x 1 ) \ = 2 x 1 cos x + x 2 c o s x − 2 = 2 x 2 x x c o s x + 2 c o s ( x − 2 ) Hence (B) is the correct answer.

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDerivatives (Newton- Leibnitz)Easy2 min

MathematicsEasysingle choice

If $f (x) = \int_{1/ x}^{x} cos t^{2} d t (x > 0)$ then $\frac{df ( x )}{d x}$ is

Options:

Answer:

Solution:

$\frac{df ( x )}{d x} = cos (x)^{2} \frac{d x}{d x} - cos (\frac{1}{x})^{2} \cdot \frac{d}{d x} (\frac{1}{x})$ \ $= \frac{1}{2 x} cos x + \frac{c o s x ^{- 2}}{x ^{2}} = \frac{x x c o s x + 2 c o s ( x ^{- 2} )}{2 x ^{2}}$

Hence (B) is the correct answer.

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Derivatives (Newton- Leibnitz)

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