# Recent questions tagged definite integrals

### Suppose $f:R\rightarrow R$ is a differentiable function and $f(1)=4$.Then value of $\lim\limits_{x\to 1}\int\limits_4^{f(x)}\large\frac{2t}{x-1}$$dt is 1 answer ### \lim\limits_{n\to \infty}\sum\limits_{r=1}^n\large\frac{\pi}{n}$$\sin\large\frac{\pi r}{n}$ is

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