If $f\left( x \right) = \mathop {\lim }\limits_{y \to x} \,\,\frac{{{{\sin }^2}y\,\, - \,\,{{\sin }^2}\,\,x}}{{{y^2}\,\, - \,\,{x^2}}}$, then $\smallint 4x\,\,\;f\left( x \right)\,\,dx$ is equal to

$ - \,2\,\,\cos \,\,2x\,\, + \,\,c$

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Analyzing +4 | -1

f\left( x \right) = \lim\limits_{y \to x} \,\,\frac{{{{\sin }^2}y\,\, - \,\,{{\sin }^2}\,\,x}}{{{y^2}\,\, - \,\,{x^2}}}

, then

\int 4x\,\,\;f\left( x \right)\,\,dx

is equal to

View answer and explanation

Correct option: C

- \,\cos \,\,2x\,\, + \,\,c

Option C is correct because after applying L'Hôpital's rule and integrating, the result is

- \,\cos \,2x\,\, + \,\,c

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