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# Help: Continuity of function 2

Let $$\displaystyle f\left( x \right) =\int _{ 0 }^{ x }{ t\sin { \frac { 1 }{ t } }\ dt }$$, then the number of points of discontinuity of $$f\left( x \right)$$ in $$\left( 0,\pi \right)$$ is $$\text{__________}$$.

7 months, 1 week ago

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We have $$f'(x)=x \sin \frac{1}{x}$$, which exists and is continuous everywhere in $$(0,\pi)$$ (Check that $$\lim_{x \to 0}x \sin \frac{1}{x}=0$$). Thus the function $$f(x)$$ has no point of discontinuity in the interval $$(0,\pi)$$. · 7 months, 1 week ago

@parv mor · 7 months, 1 week ago