Solve the Following Questions


If $f: \mathbf{R} \rightarrow \mathbf{R}$ is given by $f(\mathrm{x})=\mathrm{x}+1$, then the value of $\lim _{\mathrm{n} \rightarrow \infty} \frac{1}{\mathrm{n}}\left[f(0)+f\left(\frac{5}{\mathrm{n}}\right)+f\left(\frac{10}{\mathrm{n}}\right)+\ldots .+f\left(\frac{5(\mathrm{n}-1)}{\mathrm{n}}\right)\right]$ is :

  1. $\frac{3}{2}$

  2. $\frac{5}{2}$

  3. $\frac{1}{2}$

  4. $\frac{7}{2}$

Correct Option: , 4


$I=\sum_{r=0}^{n-1} f\left(\frac{5 r}{n}\right) \frac{1}{n}$

$I=\int_{0}^{1} f(5 x) d x$

$I=\int_{0}^{1}(5 x+1) d x$

$I=\left[\frac{5 x^{2}}{2}+x\right]_{0}^{1}$


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now