Evaluate the following integrals as limit of sum: `int_0^(3.)(2x^2+3x+5)dx`

Explanation

let `f(x) =2 x^{2}+3 x+5 \text { i.e } a=0, b=3, n h=3-0=3 `


`\therefore \int_{0}^{3}(2 x^{2}+3 x+5) d x=\lim _{h arrow 0} h[f(0)+f(0+h)+f(0+2 h)+\cdots+f(0+(n-1) h)] `



`=\lim _{h arrow 0} h[5+(2 h^{2}+3 h+5)+(8 h^{2}+6 h+5)+\cdots+\{2(n-1)^{2} h^{2}+3(n-1) h+5\}] `



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