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Can u explain limits of sum method in definite integration step wise?

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Solution: Limit of Sum

$int_a^bf(x)hspace0.1cmdx=lim_n oinfty h[f(a+h)+f(a+2h)+..........+f(a+nh)]$

When $n o infty$ , $h o0$ and $nh=b-a$

$(1)$ Express the given series in the form $sum (1/n)f(r/n)$

$(2)$ Then the limit is its sum when $n o infty$ , $lim_n oinfty sum (1/n)f(r/n)$

$(3)$ Replace $(r/n)$ by $x$ and $1/n$ by $dx$ and $lim_x oinfty sum$ by the sign of $int$ .

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Deependra Verma

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