Evaluate the following definite integral
$integral subscript 1 superscript 2 left parenthesis 4 straight x cubed minus 5 straight x squared plus 6 straight x plus 9 right parenthesis space dx.$

Solution

Let I = $integral subscript 1 superscript 2 left parenthesis 4 straight x cubed minus 5 straight x squared plus 6 straight x plus 9 right parenthesis space dx$
$equals space open square brackets fraction numerator 4 straight x to the power of 4 over denominator 4 end fraction minus fraction numerator 5 straight x cubed over denominator 3 end fraction plus fraction numerator 6 straight x squared over denominator 2 end fraction plus 9 straight x close square brackets subscript 1 superscript 2 space equals space open square brackets straight x to the power of 4 minus 5 over 3 straight x cubed plus 3 straight x squared plus 9 straight x close square brackets subscript 1 superscript 2 equals space open parentheses 16 minus 40 over 3 plus 12 plus 18 close parentheses space minus space open parentheses 1 minus 5 over 3 plus 3 plus 9 close parentheses space equals space 32 2 over 3 minus 11 1 third space equals space 21 1 third$

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Integrals

Evaluate the following definite integral
$integral subscript 1 superscript 2 left parenthesis 4 straight x cubed minus 5 straight x squared plus 6 straight x plus 9 right parenthesis space dx.$

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