# 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 $$\text{__________}$$.

2 years, 4 months 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 $$(0,\pi)$$.

- 2 years, 3 months ago

- 2 years, 4 months ago

@Rishabh Cool. I have been trying this one for sometime,

- 2 years, 4 months ago