Evaluate the following definite integrals as limit of sums.
$integral subscript 2 superscript 3 straight x squared dx$

Solution

Let I = $integral subscript 2 superscript 3 straight x squared dx$
Since $integral straight x squared dx space equals space straight x cubed over 3 space equals space straight F left parenthesis straight x right parenthesis comma space say.$
$therefore$ by second fundamental theorem,
I = F(3) - F(2) = $fraction numerator left parenthesis 3 right parenthesis cubed over denominator 3 end fraction minus fraction numerator left parenthesis 2 right parenthesis cubed over denominator 3 end fraction space equals space 9 minus 8 over 3 space equals space 19 over 3$

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Integrals

Evaluate the following definite integrals as limit of sums.
$integral subscript 2 superscript 3 straight x squared dx$

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