Evaluate the following definite integrals as limit of sums. `int0 5(x+1)""dx`

Explanation

We have, `\int_{0}^{5}(x+1) d x=\lim _{n \rightarrow \infty} h[\sum_{r=0}^{n-1} f(a+r . h]=\lim _{n \rightarrow \infty}-\frac{5}{n}[\sum_{r=0}^{n-1}(r(\frac{5}{n})+1]`


`\because h=\frac{5-0}{n} \quad f(x)=x+1`




`=\frac{5}{{n}}`


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