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Evaluate the following definite integra...

Evaluate the following definite integrals as limit of sums.`int_0^5(x+1)dx`

Text Solution

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We have,` int_0^5​(x+1)dx=lim_(N->oo) h[sum_(i=0)^(n-1)f(a+r.h)]]=lim_(N->oo) (5/n)[sum_(i=0)^(n-1)(r(5/n)+1)]]`
Since `h=5/n`
=`5/n`
=`lim_(N->oo) [sum_(i=0)^(n-1) (25/n^2)*​r+(5/n)​(.n−1)]`
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